multi adjoint t concept lattices the t concept lattice is introduced as a set of triples associated to graded tabular information interpreted in a non commutative fuzzy logic following the general techniques of formal concept analysis and based on the works by georgescu and popescu given a non commutative conjunctor it is possible to provide generalizations of the mappings for the intension and the extension in two different ways and this generates a pair of concept lattices in this paper we show that the information common to both concept lattices can be seen as a sublattice of the cartesian product of both concept lattices the multi adjoint framework can be applied to this general t concept lattice and its usefulness is illustrated by a working example

technical foundations of a dpll based sat solver for propositional godel logic we provide the foundations of automated deduction in the propositional godel logic the propositional godel logic is one of the simplest infinitely valued fuzzy logics which generalizes classical propositional logic we propose an extension of the davis putnam logemann loveland dpll procedure to this logic and prove its refutational soundness and finite completeness using the dpll procedure we solve the deduction problem t models phi boldsymbol t is a finite theory and boldsymbol phi a formula which covers the finite sat problem for a theory and the val problem for a formula obviously this paper serves on the one side as a technical basis for the design of a sat solver on the other side gives some preliminary theoretical results concerning the logical and computational foundations of fuzzy inference which is our main aim

three classes of minimal linear codes over the finite fields of odd characteristic minimal linear codes are a special subclass of linear codes and have significant applications in secret sharing and secure two party computation in this paper we focus on constructing minimal linear codes with frac w min w max leq frac p 1 p for any odd prime p based on a generic construction of linear codes where w min and w max denote the minimum and maximum nonzero weights in a code respectively first we present two new infinite families of minimal linear codes with two or three weights by selecting suitable subcode of linear codes which are not minimal second we also present an infinite family of minimal linear codes by employing partial spreads which can be viewed as a generalization of the construction of ding et al in addition we determine the weight distributions of all these minimal linear codes

statistical physics of the freely jointed chain using the method of constraints proposed by s f edwards and a g goodyear j phys a 5 965 1972 5 1188 1972 we do a complete calculation of the canonical partition function of a freely jointed chain fjc from its classical hamiltonian we show how the constraints reduce the phase space of an ideal gas of monomers to the phase space of a fjc and how they permit one to find the canonical partition function by using this function it is possible to study thermodynamical properties of fjc s and to build other thermodynamical ensembles via laplace transforms thus we define a grand canonical ensemble where the monomer number of the fjc can fluctuate in this ensemble the fjc of infinite length is the asymptotic state at low and high temperatures the critical exponents ensuremath gamma and ensuremath nu for fjc s are calculated and found to be equal to the gaussian polymer exponents connections between the properties of fjc s and random walks on regular lattices are also discussed textcopyright 1996 the american physical society

α β ordered linear resolution of intuitionistic fuzzy propositional logic abstract this paper presents an approach for resolution based automated reasoning in intuitionistic fuzzy propositional logic ifl in ifl systems every ifl formula with both a truth degree and a falsity degree at the same time can be transformed into ifl generalized clause based on some equivalent properties in a finite time with assumed thresholds we judge whether each ifl literal of ifl generalized clauses is satisfiable or not according to the ifl literal s satisfiability the ifl literals can be divided into two classes i e similar literals and complementary literals we use the structure of the linear resolution which only has a center line and a side line to restrict the resolution clauses in every resolution procedure ifl framed literals recording information of resolved literals instead of storing them in a memory can be used to reduce the number of possible resolutions and improve the efficiency of the resolution the empty clause can be obtained with layer resolution where the threshold can be changed the soundness and completeness of ordered linear resolution are proved and an illustrative example is given to verify the ordered linear resolution algorithm and demonstrate its effectiveness

secret sharing schemes from binary linear codes in principle every linear code can be used to construct a secret sharing scheme however in general determining the access structure of the scheme is very hard on the other hand finding error correcting codes that produce secret sharing schemes with efficient access structures is also difficult in this paper we study a set of minimal codewords for certain classes of binary linear codes and then determine the access structure of secret sharing schemes based on these codes furthermore we prove that the secret sharing schemes obtained are democratic in the sense that every participant is involved in the same number of minimal access sets

a strengthening of the assmus mattson theorem let w sub 1 d w sub 2 w sub s be the weights of the nonzero codewords in a binary linear n k d code c and let w sub 1 w sub 2 w sub 3 be the nonzero weights in the dual code c1 let t be an integer in the range 0 or d 4 then either the words of any nonzero weight w sub i form a t 1 design or else the codewords of minimal weight d form a 1 2 t t 2 design if in addition c is self dual with all weights divisible by 4 then the codewords of any given weight w sub i form either a t 1 design or a 1 2 t t 2 design the proof avoids the use of modular forms

association schemes and coding theory this paper contains a survey of association scheme theory with its algebraic and analytical aspects and of its applications to coding theory in a wide sense it is mainly concerned with a class of subjects that involve the central notion of the distance distribution of a code special emphasis is put on the linear programming method inspired by the macwilliams transform this produces upper bounds for the size of a code with a given minimum distance and lower bounds for the size of a design with a given strength the most specific results are obtained in the case where the underlying association scheme satisfies certain well defined polynomial properties this leads one into the realm of orthogonal polynomial theory in particular some universal bounds are derived for codes and designs in polynomial type association schemes throughout the paper the main concepts methods and results are illustrated by two examples that are of major significance in classical coding theory namely the hamming scheme and the johnson scheme other topics that receive special attention are spherical codes and designs and additive codes in translation schemes including z sub 4 additive binary codes

linear codes from some 2 designs a classical method of constructing a linear code over mathrm gf q with a t design is to use the incidence matrix of the t design as a generator matrix over mathrm gf q of the code this approach has been extensively investigated in the literature in this paper a different method of constructing linear codes using specific classes of 2 designs is studied and linear codes with a few weights are obtained from almost difference sets difference sets and a type of 2 designs associated to semibent functions two families of the codes obtained in this paper are optimal the linear codes presented in this paper have applications in secret sharing and authentication schemes in addition to their applications in consumer electronics communication and data storage systems a coding theory approach to the characterization of highly nonlinear boolean functions is presented

hedge algebras an algebraic approach to structure of sets of linguistic truth values abstract it is shown that any sets of linguistic values of linguistic variables can be axiomatized which leads to a notion of hedge algebras some intuitive properties of linguistic hedges which are a basis of the axiomatization of the hedge algebras are discussed informally the characteristics of the hedge algebras depend on such a discussion and they seem to reflect the natural structure of sets of linguistic values of linguistic variables some fundamental properties of hedge algebras are examined they constitute a foundation of further development of our theory of hedge algebras and of some kind of fuzzy logic

minimal linear codes from characteristic functions minimal linear codes have interesting applications in secret sharing schemes and secure two party computation this paper uses characteristic functions of some subsets of mathbb f q to construct minimal linear codes by properties of characteristic functions we can obtain more minimal binary linear codes from known minimal binary linear codes which generalizes results of ding et al ieee trans inf theory vol 64 no 10 pp 6536 6545 2018 by characteristic functions corresponding to some subspaces of mathbb f q we obtain many minimal linear codes which generalizes results of ieee trans inf theory vol 64 no 10 pp 6536 6545 2018 and ieee trans inf theory vol 65 no 11 pp 7067 7078 2019 finally we use characteristic functions to present a characterization of minimal linear codes from the defining set method and present a class of minimal linear codes

a resolution principle based on first order lattice valued logic lf x abstract in the present paper as a continuous work about resolution principle based on lattice valued propositional logic lp x information sciences 130 2000 1 29 whose algebra of truth values is a relatively general lattice lattice implication algebra lia the lattice valued resolution principle for the corresponding first order lattice valued logic system lf x is focused firstly some concepts about lattice valued resolution principle for lf x are introduced and the herbrand theorem for lf x is proved then an resolution principle which can be used to judge if a first order lattice valued logical formula in lf x is false at a truth valued level i e false is established finally the completeness theorem of this resolution principle and the soundness theorem for the strong resolution are also proved it is hoped that the current work would serve as a foundation for constructing resolution based automated reasoning methods for lattice valued logic capable of dealing with both comparable and incomparable uncertain information

a resolution principle based on lattice valued propositional logic lp x abstract in the present paper resolution based automated reasoning theory in an l type fuzzy logic is focused concretely the resolution principle which is based on lattice valued propositional logic lp x with truth value in a logical algebra lattice implication algebra is investigated finally an resolution principle that can be used to judge if a lattice valued logical formula in lp x is always false at a truth valued level i e false is established and the theorems of both soundness and completeness of this resolution principle are also proved this will become the theoretical foundation for automated reasoning based on lattice valued logical lp x

which logic is the real fuzzy logic this paper is a contribution to the discussion of the problem whether there is a fuzzy logic that can be considered as the real fuzzy logic we give reasons for taking imtl bl email protected and ev l fuzzy logic with evaluated syntax as those fuzzy logics that should be indeed taken as the real fuzzy logics

on binary linear codes supporting t designs in this paper we present classification results on self orthogonal binary codes supporting designs therefore we use special linear forms on the intersection numbers in particular one shows that a binary self orthogonal code of distance d spl les 18 whose set of minimal weight codewords supports a 5 design has to be self dual we also prove that the codewords of any fixed weight in a 24m 22 12m 11 4m 6 type i code support a 3 design

spherically symmetric random walks in noninteger dimension a previous article proposed a new kind of random walk on a spherically symmetric lattice in arbitrary noninteger dimension d such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension this article examines the nature of spherically symmetric random walks in detail a large time asymptotic analysis of these random walks is performed and the results are used to determine the hausdorff dimension of the process exact results are obtained in terms of hurwitz functions incomplete zeta functions for the probability of a walker going from one region of the spherical lattice to another finally it is shown that the probability that the paths of k independent random walkers will intersect vanishes in the continuum limit if d 2k k 1

satisfiability in many valued sentential logic is np complete abstract cook s np completeness theorem is extended to all many valued sentential logics including the infinite valued calculus of ukasiewicz

canonical partition functions of freely jointed chains the freely jointed chain is a simple off lattice ideal model of a heteropolymer we show how to compute the canonical partition function of this model exactly for all physical primary structures degree of polymerization and space dimensions greater than or equal to 2 the canonical partition function of this model of a heteropolymer has an analytical expression involving a complicated multiple hypergeometric function to obtain some accurate approximations we develop and use the independent motion approximation ima

two new families of two weight codes we construct two new infinite families of trace codes of dimension 2m over the ring mathbb f p u mathbb f p with u 2 u when p is an odd prime they have the algebraic structure of abelian codes their lee weight distribution is computed by using gauss sums by gray mapping we obtain two infinite families of linear p ary codes of respective lengths p m 1 2 and 2 p m 1 2 when m is singly even the first family gives five weight codes when m is odd and p equiv 3 pmod 4 the first family yields p ary two weight codes which are shown to be optimal by application of the griesmer bound the second family consists of two weight codes that are shown to be optimal by the griesmer bound whenever p 3 and m ge 3 or p ge 5 and m ge 4 applications to secret sharing schemes are given

secret sharing schemes from three classes of linear codes secret sharing has been a subject of study for over 20 years and has had a number of real world applications there are several approaches to the construction of secret sharing schemes one of them is based on coding theory in principle every linear code can be used to construct secret sharing schemes but determining the access structure is very hard as this requires the complete characterization of the minimal codewords of the underlying linear code which is a difficult problem in general in this paper a sufficient condition for all nonzero codewords of a linear code to be minimal is derived from exponential sums some linear codes whose covering structure can be determined are constructed and then used to construct secret sharing schemes with nice access structures

a linear code based on resilient boolean maps whose dual is a platform for a robust secret sharing scheme abstract a linear code based on resilient maps on vector spaces over finite fields is introduced and lower bounds for its minimal distance are given the dual code is used to define a secret sharing scheme sss according to massey construction since the dual code satisfies the conditions stated by padro and saez the generalization to a vector space sss is robust against cheaters

a new upper bound on the minimal distance of self dual codes it is shown that the minimal distance d of a binary self dual code of length n or 74 is at most 2 n 6 10 this bound is a consequence of some new conditions on the weight enumerator of a self dual code obtained by considering a particular translate of the code called its shadow these conditions also enable one to find the highest possible minimal distance of a self dual code for all n or 60 to show that self dual codes with d or 22 with d or 8 exist precisely for n 24 32 and n or 26 and with d or 10 exist precisely for n or 46 and to show that there are exactly eight self dual codes of length 32 with d 8 several of the self dual codes of length 34 have trivial group this appears to be the smallest length where this can happen

on secret sharing systems a secret sharing system permits a secret to be shared among n trustees in such a way that any k of them can recover the secret but any k 1 have complete uncertainty about it a linear coding scheme for secret sharing is exhibited which subsumes the polynomial interpolation method proposed by shamir and can also be viewed as a deterministic version of blakley s probabilistic method bounds on the maximum value of n for a given k and secret size are derived for any system linear or nonlinear the proposed scheme achieves the lower bound which for practical purposes differs insignificantly from the upper bound the scheme may be extended to protect several secrets methods to protect against deliberate tampering by any of the trustees are also presented

a framework for linguistic modelling a new framework for linguistic reasoning is proposed based on a random set model of the degree of appropriateness of a label labels are assumed to be chosen from a finite predefined set of labels and the set of appropriate labels for a value is defined as a random set valued function from a population of individuals into the set of subsets of labels appropriateness degrees are then evaluated relative to the distribution on this random set where the appropriateness degree of a label corresponds to the probability that it is contained in the set of appropriate labels this interpretation is referred to as label semantics a natural calculus for appropriateness degrees is described which is weakly functional while taking into account the logical structure of expressions given this framework it is shown that a bayesian approach can be adopted in order to infer probability distributions on the underlying variable given constraints both in the form of linguistic expressions and mass assignments in addition two conditional measures are introduced for evaluating the appropriateness of a linguistic expression given other linguistic information

five families of three weight ternary cyclic codes and their duals as a subclass of linear codes cyclic codes have applications in consumer electronics data storage systems and communication systems as they have efficient encoding and decoding algorithms in this paper five families of three weight ternary cyclic codes whose duals have two zeros are presented the weight distributions of the five families of cyclic codes are settled the duals of two families of the cyclic codes are optimal

fuzzy logic of lukasiewicz logic a clarification pavelka 10 had shown in 1979 that the only natural way of formalizing fuzzy logic for truth value in the unit interval 0 1 is by using lukasiewicz s implication operator a b min 1 1 a b or some isomorphic form of it a considerable number of other papers around the same time had attempted to formulate alternative definitions for a b by giving intuitive justifications for them there continues to be some confusion however even today about the right notion of fuzzy logic much of this has its origin in the use of improper and or and the not operations and a misunderstanding of some of the key differences between proofs or inferencing in fuzzy logic and those in lukasiewicz s logic we point out the need for defining the strong conjunction operator in connection with fuzzy modus ponens rule and why we do not need the fuzzy syllogism rule we also point out the shortcomings of many of the alternative definitions of a b which indicate further support for pavelka s result we hope that these discussions help to clarify the misconceptions about fuzzy logic

are fuzzy sets a reasonable tool for modeling vague phenomena in the paper the indeterminacy phenomenon is discussed that is a phenomenon having two facets uncertainty and vagueness we argue that fuzzy sets are a reasonable mathematical tool for modeling of the latter the necessary sound foundations of their theory can now be more easily established because of significant progress reached in the formal theory of fuzzy logic further direction in the development of fuzzy set theory is also discussed

a family of five weight cyclic codes and their weight enumerators cyclic codes are a subclass of linear codes and have applications in consumer electronics data storage systems and communication systems as they have efficient encoding and decoding algorithms in this paper a family of p ary cyclic codes whose duals have three pairwise nonconjugate zeros is proposed the weight distribution of this family of cyclic codes is determined it turns out that the proposed cyclic codes have five nonzero weights

reductions for non clausal theorem proving this paper presents the tas methodology as a new framework for generating non clausal automated theorem provers we present a complete description of the atp for classical propositional logic named tas d but the ideas which make use of implicants and implicates can be extended in a natural manner to first order logic and non classical logics the method is based on the application of a number of reduction strategies on subformulas in a rewrite system style in order to reduce the complexity of the formula as much as possible before branching specifically we introduce the concept of complete reduction and extensions of the pure literal rule and ofthe collapsibility theorems these strategies allow to limit the size ofthe search space in addition tas d is a syntactical countermodel construction as an example of the power of tas d we study a class of formulas which has linear proofs in the number of branchings when either resolution or dissolution with factoring is applied when applying our method to these formulas we get proofs without branching in addition some experimental results are reported copyright 2001 elsevier science b v

holonomic constraints an analytical result systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with hamiltonian or lagrangian dynamics the influence of holonomic constraints in equations of motions is taken into account by using lagrange multipliers finding the value of the lagrange multipliers allows us to compute the forces induced by the constraints and therefore to integrate the equations of motions of the system computing analytically the lagrange multipliers for a constrained system may be a difficult task that depends on the complexity of systems for complex systems it is most of the time impossible to achieve in computer simulations some algorithms using iterative procedures estimate numerically lagrange multipliers or constraint forces by correcting the unconstrained trajectory in this work we provide an analytical computation of the lagrange multipliers for a set of linear holonomic constraints with an arbitrary number of bonds of constant length in the appendix explicit formulae are shown for lagrange multipliers for systems having 1 2 3 4 and 5 bonds of constant length linearly connected

on the covering structures of two classes of linear codes from perfect nonlinear functions in this paper the weight distributions of two classes of linear codes based on all known explicit perfect nonlinear functions from fqm to itself are determined using a unified approach all the minimal codewords of these codes are characterized according to their weights which suggests that their covering structures are determined finally all the minimal access sets of the secret sharing schemes based on their dual codes are obtained

l valued propositional logic l vpl in this paper two types of gradational l type lattice valued propositional logic l v p l with truth values in a lattice implication algebra are introduced and some fundamental questions of them such as semantics syntax and compactness are investigated and where the l type a soundness theorem a b completeness theorem a b consistent theorem and a b q deduction theorem are also proved

determinization of fuzzy automata with membership values in complete residuated lattices in this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices in comparison with the previous methods developed by belohlavek r belohlavek determinism and fuzzy automata information sciences 143 2002 205 209 and li and pedrycz y m li w pedrycz fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids fuzzy sets and systems 156 2005 68 92 our method always gives a smaller automaton and in some cases when the previous methods result in infinite automata our method can result in a finite one we also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them and in particular to the concept of the nerode s fuzzy right congruence of a fuzzy automaton which we introduce and study here

a resolution like strategy based on a lattice valued logic as the use of nonclassical logics becomes increasingly important in computer science artificial intelligence and logic programming the development of efficient automated theorem proving based on nonclassical logic is currently an active area of research this paper aims at the resolution principle for the pavelka type fuzzy logic 1979 pavelka showed that the only natural way of formalizing fuzzy logic for truth values in the unit interval 0 1 is by using the lukasiewicz s implication operator a spl rarr b min 1 1 a b or some isomorphic forms of it hence we first focus on the resolution principle for the lukasiewicz logic l sub spl aleph with 0 1 as the truth valued set some limitations of classical resolution and resolution procedures for fuzzy logic with kleene implication are analyzed then some preliminary ideals about combining resolution procedure with the implication connectives in l sub spl aleph are given moreover a resolution like principle in l sub spl aleph is proposed and the soundness theorem of this resolution procedure is also proved second we use this resolution like principle to horn clauses with truth values in an enriched residuated lattice and consider the l type fuzzy prolog

on the refutational completeness of signed binary resolution and hyperresolution signed binary resolution and hyperresolution belong to the basic resolution proof methods both the resolution methods are refutation sound and under some finitary restrictions refutation complete our aim is to investigate their refutational completeness in a more general case we shall assume that clausal theories may be countable sets and the set of truth values an arbitrary one there are unsatisfiable countable clausal theories for which there do not exist refutations by signed binary resolution and hyperresolution we propose a criterion on the existence of a refutation of an unsatisfiable countable clausal theory by the investigated resolution methods two important applications of the achieved results to automated deduction in signed logic herbrand s theorem and a signed davis putnam logemann loveland dpll procedure will be discussed

multiary α resolution principle for a lattice valued logic this paper focuses on resolution based automated reasoning theory in a lattice valued logic system with truth values that are defined in a lattice valued logical algebraic structure lattice implication algebras lias which essentially aims to extend the classical logic to handle automated deduction under an uncertain environment concretely we investigate a generalization of the known conjunctive normal form cnf in the classical logic representation that we call the generalized conjunctive normal form gcnf which aims to characterize the constants and implication connectives that are essentially different from the ones in classical logic we then extend the established resolution principle at a certain truth value level called resolution in this lattice valued logic to a more general form i e from binary resolution to multiary resolution the extension to multiary resolution starts from lattice valued propositional logic lp x while its theorems of both soundness and completeness are proved multiary resolution principle is then further established in the corresponding lattice valued first order logic lf x along with its soundness theorem lifting lemma and completeness theorem meanwhile an important result that multiary resolution principle in lf x can be equivalently transformed into that in lp x to some extent is obtained all these works will theoretically support the establishment of an automated reasoning algorithm and its implementation with further applications into automated deduction and decision making problems under uncertainty

approximate reasoning by similarity based sld resolution in gerla and sessa fuzzy logic and soft computing kluwer norwell 1999 pp 19 31 a methodology that allows to manage uncertain and imprecise information in the frame of the declarative paradigm of logic programming has been proposed with this aim a similarity relation r between function and predicate symbols in the language of a logic program is considered approximate inferences are then possible since similarity relation allows us to manage alternative instances of entities that can be considered equal with a given degree the declarative semantics of the proposed transformation technique of logic programs is analyzed the notion of fuzzy least herbrand model is also introduced in this paper the corresponding operational semantics is provided by introducing a modified version of sld resolution this top down refutation procedure overcomes failure situations in the unification process by using the similarity relation a generalized notion of most general unifier provides a numeric value which gives a measure of the exploited approximation in this way the sld resolution is enhanced since it is possible both to handle uncertain or imprecise information and to compute approximate answer substitutions with an associated approximation degree when failures of the exact inference process occur it can lead to the implementation of a more general prolog interpreter without detracting from the elegance of the language

random walks in noninteger dimension one can define a random walk on a hypercubic lattice in a space of integer dimension d for such a process formulas can be derived that express the probability of certain events such as the chance of returning to the origin after a given number of time steps these formulas are physically meaningful for integer values of d however these formulas are unacceptable as probabilities when continued to noninteger d because they give values that can be greater than 1 or less than 0 in this paper a different kind of random walk is proposed which gives acceptable probabilities for all real values of d this d dimensional random walk is defined on a rotationally symmetric geometry consisting of concentric spheres the exact result is given for the probability of returning to the origin for all values of d in terms of the riemann zeta function this result has a number theoretic interpretation

the art of signaling fifty years of coding theory in 1948 shannon developed fundamental limits on the efficiency of communication over noisy channels the coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero fifty years later codes for the gaussian channel have been discovered that come close to these fundamental limits there is now a substantial algebraic theory of error correcting codes with as many connections to mathematics as to engineering practice and the last 20 years have seen the construction of algebraic geometry codes that can be encoded and decoded in polynomial time and that beat the gilbert varshamov bound given the size of coding theory as a subject this review is of necessity a personal perspective and the focus is reliable communication and not source coding or cryptography the emphasis is on connecting coding theories for hamming and euclidean space and on future challenges specifically in data networking wireless communication and quantum information theory

narrow sense bch codes over mathrm gf q with length n frac q m 1 q 1 cyclic codes are widely employed in communication systems storage devices and consumer electronics as they have efficient encoding and decoding algorithms bch codes as a special subclass of cyclic codes are in most cases among the best cyclic codes a subclass of good bch codes are the narrow sense bch codes over mathrm gf q with length n q m 1 q 1 little is known about this class of bch codes when q 2 the objective of this paper is to study some of the codes within this class in particular the dimension the minimum distance and the weight distribution of some ternary bch codes with length n 3 m 1 2 are determined in this paper a class of ternary bch codes meeting the griesmer bound is identified an application of some of the bch codes in secret sharing is also investigated

an annotated logic theorem prover for an extended possibilistic logic in this paper we present a theorem prover for possibilistic logic extended with fuzzy constants and fuzzily restricted quantifiers first of all we propose a representation for this logic in terms of horn clauses we then show how to transform this horn clause formalism into the generalized annotated logic formalism proposed by kifer and subrahmanian in 1992 specifically the valuation in a possibilistic clause generates the annotation which will be attached to the head of the annotated clause we also show how the inference rules of this possibilistic logic can be translated in terms of the mechanisms provided by this annotated logic finally we discuss the implementation of a theorem prover for this possibilistic logic now translated to annotated logic in system komet a large purpose system which has generalized annotated logic as its underlying framework in this paper we also present proofs relative to the theoretical issues and some examples implemented in komet

freely jointed chains in external potentials analytical computations freely jointed chains in external potentials are crude representations of macromolecular systems in interaction with electrostatic fields surfaces walls and interfaces we show how the canonical partition function of these models can be computed analytically and how the independent motion approximation ima may be applied in particular the chain stretched at both ends is studied with ima and new results are obtained for entropic elastic constants and force extension relations including the dependence on the degree of polymerization these new results are in good agreement with molecular dynamics computations

binary resolution over complete residuated stone lattices this paper extends previous results obtained for binary resolution proof method over complete boolean lattices we shall assume that truth values form a complete residuated stone lattice in addition we investigate binary resolution over residuated lattices with strict negation the refutational soundness and completeness of the generalised resolution proof method will be proved finally we discuss the boundaries of the refutational completeness over arbitrary residuated lattices

graded many valued resolution with aggregation abstract the aim of this paper is to give a sound resolution deduction rule in many valued logic with truth value range 0 1 and with arbitrary connectives and graded information we introduce and study the resolution truth function which will evaluate the truth value of the result of resolution conditions under which this function yields an aggregation operator will be given

ordered chaining calculi for first order theories of transitive relations we propose inference systems for binary relations that satisfy composition laws such as transitivity our inference mechanisms are based on standard techniques from term rewriting and represent a refinement of chaining methods as they are used in the context of resolution type theorem proving we establish the refutational completeness of these calculi and prove that our methods are compatible with the usual simplification techniques employed in refutational theorem provers such as subsumption or tautology deletion various optimizations of the basic chaining calculus will be discussed for theories with equality and for total orderings a key to the practicality of chaining methods is the extent to which so called variable chaining can be avoided we demonstrate that rewrite techniques considerably restrict variable chaining and that further restrictions are possible if the transitive relation under consideration satisfies additional properties such as symmetry but we also show that variable chaining cannot be completely avoided in general

an algebraic approach to linguistic hedges in zadeh s fuzzy logic the paper addresses the mathematical modelling of domains of linguistic variables i e term sets of linguistic variables in order to obtain a suitable algebraic structure for the set of truth values of zadeh s fuzzy logic we shall give a unified algebraic approach to the natural structure of domains of linguistic variables which was proposed by ho and wechler fuzzy sets and systems 35 1990 281 and then by ho and nam proc ncst vietnam 9 1 1997 15 logic algebra and computer science vol 46 banach center publications pwn warsaw 1999 p 63 in this approach every linguistic domain can be considered as an algebraic structure called hedge algebra because properties of its unary operations reflect semantic characteristics of linguistic hedges many fundamental properties of refined hedge algebras rh algebras are examined especially it is shown that every rh algebra of a linguistic variable with a chain of the primary terms is a distributive lattice rh algebras with exactly two distinct primary terms one being an antonym of the other will also be investigated and they will be called symmetrical rh algebras it is shown that a class of finite symmetrical rh algebras has a rich enough algebraic structure

rough set theory applied to lattice theory in this paper we intend to study a connection between rough sets and lattice theory we introduce the concepts of upper and lower rough ideals filters in a lattice then we offer some of their properties with regard to prime ideals filters the set of all fixed points compact elements and homomorphisms

minimal vectors in linear codes minimal vectors in linear codes arise in numerous applications particularly in constructing decoding algorithms and studying linear secret sharing schemes however properties and structure of minimal vectors have been largely unknown we prove basic properties of minimal vectors in general linear codes then we characterize minimal vectors of a given weight and compute their number in several classes of codes including the hamming codes and second order reed muller codes further we extend the concept of minimal vectors to codes over rings and compute them for several examples turning to applications we introduce a general gradient like decoding algorithm of which minimal vectors decoding is an example the complexity of minimal vectors decoding for long codes is determined by the size of the set of minimal vectors therefore we compute this size for long randomly chosen codes another example of algorithms in this class is given by zero neighbors decoding we discuss relations between the two decoding methods in particular we show that for even codes the set of zero neighbors is strictly optimal in this class of algorithms this also implies that general asymptotic improvements of the zero neighbors algorithm in the frame of gradient like approach are impossible we also discuss a link to secret sharing schemes

completely non clausal theorem proving the proof procedure we describe operates on quantifier free formulas of the predicate calculus which are not truth functionally normalized in any way the procedure involves a single inference rule called nc resolution and is shown to be complete completeness is also obtained for a simple restriction on the rule s application examples are given using nc resolution to derive a logic program from its specification and to execute a program specification in its original form

lattice implication ordered semigroups from the viewpoint of semantics lattice implication algebras provide a basis to establish lattice valued logic with truth value in a relatively general lattice in this paper we first introduce two notions of lattice implication n ordered semigroup and lattice implication p ordered semigroup which induced by lattice implication algebras secondly we study some of their basic properties and prove that a lattice implication n ordered semigroup is a residuated semigroup and a lattice implication p ordered semigroup is an arithmetic lattice ordered semigroup we also define the homomorphism mapping between lattice implication n ordered semigroups finally we discuss some properties of filters and sl ideals in lattice implication n ordered semigroups and lattice implication p ordered semigroups

seven classes of three weight cyclic codes cyclic codes are a subclass of linear codes and have applications in consumer electronics data storage systems and communication systems as they have efficient encoding and decoding algorithms compared with linear block codes in this paper seven classes of three weight cyclic codes over gf p whose duals have two zeros are presented where p is an odd prime the weight distributions of the seven classes of cyclic codes are settled some of the cyclic codes are optimal in the sense that they meet certain bounds on linear codes the application of these cyclic codes in secret sharing is also considered

extending the t design concept let b be a family of k subsets of a v set v with 1 less than or equal to k less than or equal to v 2 given only the inner distribution of b i e the number of pairs of blocks that meet in j points with j 0 1 k we are able to completely describe the regularity with which b meets an arbitrary t subset of v for each order t with 1 less than or equal to t less than or equal to v 2 this description makes use of a linear transform based on a system of dual hahn polynomials with parameters v k t the main regularity parameter is the dimension of a well defined subspace of r t 1 called the t form space of b this subspace coincides with r t 1 if and only if b is a t design we show that the t form space has the structure of an ideal and we explain how to compute its canonical generator

representing lattices using many valued relations this paper provides a representation theorem of lattices using many valued relations we show that any many valued relation can be associated to a unique lattice which is a meet sublattice of a product of chains conversely to any lattice we can associate a many valued relation such that its associated lattice is isomorphic to the initial one thereby we obtain a representation theorem of lattices using many valued relations moreover since several many valued relations might have the same associated lattice we give a characterization of the minimal many valued relation that can be associated to a lattice we then sketch a polynomial time algorithm which computes such a minimal relation from either a lattice or an arbitrary relation this representation presents several advantages it is smaller than the usual binary representation all known reconstruction algorithms working on binary relation can be used without loss of efficiency it can be used by existing data mining processes

algebraic structures in fuzzy logic abstract common features in various fuzzy logical systems are investigated it turns out that adjoint couples and residuated lattices are very often present though not always explicitly expressed some minor new results are also proved

filter based resolution principle for lattice valued propositional logic lp x as one of most powerful approaches in automated reasoning resolution principle has been introduced to non classical logics such as many valued logic however most of the existing works are limited to the chain type truth value fields lattice valued logic is a kind of important non classical logic which can be applied to describe and handle incomparability by the incomparable elements in its truth value field in this paper a filter based resolution principle for the lattice valued propositional logic lp x based on lattice implication algebra is presented where filter of the truth value field being a lattice implication algebra is taken as the criterion for measuring the satisfiability of a lattice valued logical formula the notions and properties of lattice implication algebra filter of lattice implication algebra and the lattice valued propositional logic lp x are given firstly the definitions and structures of two kinds of lattice valued logical formulae i e the simple generalized clauses and complex generalized clauses are presented then finally the filter based resolution principle is given and after that the soundness theorem and weak completeness theorems for the presented approach are proved

linear codes with two or three weights from weakly regular bent functions linear codes with a few weights have applications in consumer electronics communication data storage system secret sharing authentication codes association schemes and strongly regular graphs this paper first generalizes the method of constructing two weight and three weight linear codes of ding et al and zhou et al to general weakly regular bent functions and determines the weight distributions of these linear codes it solves an open problem proposed by ding et al furthermore this paper constructs new linear codes with two or three weights and presents their weight distributions they contain some optimal codes meeting certain bound on linear codes

codes differentially delta uniform functions and t designs boolean functions coding theory and t designs have close connections and interesting interplay a standard approach to constructing t designs is the use of linear codes with certain regularity the assmus mattson theorem and the automorphism groups are two ways for proving that a code has sufficient regularity for supporting t designs however some linear codes hold t designs although they do not satisfy the conditions in the assmus mattson theorem and do not admit a t transitive or t homogeneous group as a subgroup of their automorphisms the major objective of this paper is to develop a theory for explaining such codes and obtaining such new codes and hence new t designs to this end a general theory for punctured and shortened codes of linear codes supporting t designs is established a generalized assmus mattson theorem is developed and a link between 2 designs and differentially delta uniform functions and 2 designs is built with these general results binary codes with new parameters and explicit weight distributions are obtained new 2 designs and steiner system s 2 4 2 n are produced in this paper

hamming weights of the duals of cyclic codes with two zeros cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms in this paper let bbb f r be a finite field with r q m suppose that g 1 g 2 in bbb f r are not conjugates over bbb f q operatorname ord g 1 n 1 operatorname ord g 2 n 2 d gcd n 1 n 2 and n n 1n 2 d let bbb f q g 1 bbb f q m 1 bbb f q g 2 bbb f q m 2 and text t i denote the trace function from bbb f q m i to bbb f q for i 1 2 we define a cyclic code mathcal c q m n 1 n 2 c a b a in bbb f q m 1 b in bbb f q m 2 where c a b text t 1 ag 1 0 text t 2 bg 2 0 text t 1 ag 1 1 text t 2 bg 2 1 ldots text t 1 ag 1 n 1 text t 2 bg 2 n 1 we mainly use gauss periods to present the weight distribution of the cyclic code mathcal c q m n 1 n 2 as applications we determine the weight distribution of cyclic code mathcal c q m q m 1 1 q m 2 1 with gcd m 1 m 2 1 in particular it is a three weight cyclic code if gcd q 1 m 1 m 2 1 we also explicitly determine the weight distributions of some classes of cyclic codes including several classes of four weight cyclic codes

binary resolution over boolean lattices abstract we propose a binary resolution system over boolean lattices we shall assume that truth values form a complete boolean lattice l where its supremum operator is infinitely distributive over the infimum one binary l resolution will operate on graded clauses a graded clause is a pair of the form l 1 l n c where l i are literals and c is a truth degree in l the refutational soundness and completeness of the proposed resolution proof method will be proved

hyperresolution for godel logic with truth constants abstract in the paper we generalise the well known hyperresolution principle to the general first order godel logic with explicit partial truth we propose a hyperresolution calculus suitable for automated deduction in a useful expansion of godel logic by intermediate truth constants and the equality strict order projection operators we solve the deduction problem of a formula from a countable theory in this expansion we expand godel logic by a countable set of intermediate truth constants of the form c c 0 1 our approach is based on translation of a formula to an equivalent satisfiable finite order clausal theory consisting of order clauses an order clause is a finite set of order literals of the form e 1 e 2 where e i is an atom or a truth constant or a quantified atom and is a connective equality or strict order and are interpreted by the equality and standard strict linear order on 0 1 respectively we shall investigate the canonical standard completeness where the semantics of godel logic is given by the standard g algebra and truth constants are interpreted by themselves the hyperresolution calculus is refutation sound and complete for a countable order clausal theory under a certain condition for the set of truth constants occurring in the theory as an interesting consequence we get an affirmative solution to the open problem of recursive enumerability of unsatisfiable formulae in godel logic with truth constants and the equality strict order projection operators

a linguistic multi criteria decision making approach based on logical reasoning in real decision making problems it is always more natural for decision makers to use linguistic terms to express their preferences opinions in a qualitative way among alternatives than to provide quantitative values additionally many of these decision making problems are under uncertain environments with vague and imprecise information involved following the idea of computing with words cww methodology we propose in this paper a linguistic valued qualitative aggregation and reasoning framework for multi criteria decision making problems where a linguistic valued algebraic structure is constructed for modelling the linguistic information involved in multi criteria decision making problems and a linguistic valued logic based approximate reasoning method is developed to infer the final decision making result this method takes the advantage of handling the linguistic information no matter totally ordered or partially ordered directly without numerical approximation and having a non classical logic as its formal foundation for decision making process

tableau method for residuated logic abstract residuated logic is a generalization of intuitionistic logic which does not assume the idempotence of the conjunction operator such generalized conjunction operators have proved important in expert systems in the area of approximate reasoning and in some areas of theoretical computer science here we generalize the intuitionistic tableau procedure and prove that this generalized tableau method is sound for the semantics the class of residuated algebras of residuated propositional calculus rpc since the axioms of rpc are complete for the semantics we may conclude that whenever a formula 0 is tableau provable it is deducible in rpc we present two different approaches for constructing residuated algebras which give us countermodels for some formulas which are not tableau provable the first uses the fact that the theory of residuated algebras is equational to construct quotients of free algebras the second uses finite algebras we end by discussing a number of open questions

fuzzy logic programming in this paper we consider the theory of fuzzy logic programming without negation our results cover logical systems with a wide variety of connectives ranging from t norm and conorms through conjunctors and disjunctors and their residuals to aggregation operators rules of our programs are many valued implications we emphasize that in contrast to other approaches our logic is truth functional i e according to p hajek we work in fuzzy logic in narrow sense we prove the soundness and the completeness of our formal model we deal with applications to threshold computation abduction fuzzy unification based on similarity we show that fuzzy unification based on similarities has applications to fuzzy databases and flexible querying

continued fraction as a discrete nonlinear transform the connection between a taylor series and a continued fraction involves a nonlinear relation between the taylor coefficients an and the continued fraction coefficients bn in many instances it turns out that this nonlinear relation transforms a complicated sequence an into a very simple one bn this simplification is illustrated in the context of graph combinatorics

determination of α resolution in lattice valued first order logic lf x key issues for resolution based automated reasoning in lattice valued first order logic lf x are investigated with truth values in a lattice valued logical algebraic structure lattice implication algebra lia the determination of resolution at a certain truth value level called a resolution in lf x is proved to be equivalently transformed into the determination of a resolution in lattice valued propositional logic lp x based on lia the determination of a resolution of any quasi regular generalized literals and constants under various cases in lp x is further analyzed specified and subsequently verified hence the determination of a resolution in lf x can be accordingly solved to a very broad extent which not only lays a foundation for the practical implementation of automated reasoning algorithms in lf x but also provides a key support for a resolution based automated reasoning approaches and algorithms in lia based linguistic truth valued logics

resolution and model building in the infinite valued calculus of lukasiewicz abstract we discuss resolution and its complexity in the infinite valued sentential calculus of l ukasiewicz with special emphasis on model building algorithms for satisfiable sets of clauses we prove that resolution and model building are polynomially tractable in the fragments given by horn clauses and by krom clauses i e clauses with at most two literals generalizing the pre existing literature on resolution in infinite valued logic by a positive literal we mean a negationless formula in one variable built only from the connectives we prove that the expressive power of our literals encompasses all monotone mcnaughton functions of one variable

a new fuzzy resolution principle based on the antonym abstract in this paper a new fuzzy resolution principle called antonym based fuzzy hyper resolution afhr is introduced and its completeness is proven the proposed inference rule is based on the idea of reductio ad absurdum by the antonym not by negation in the existing binary logic the proposed resolution has a meaningless range a special set that is not true and also that is not false this range should not be considered in the reasoning the advantage of afhr is that it executes effective resolution and shows flexibility for some automated reasoning we review the negation based fuzzy inference mechanism that is oriented by binary logic and firstly introduce the concept of the reductio ad absurdum by the antonym for the fuzzy resolution we shall further discuss the effects of flexibility of afhr for quadratic equations finally examples of afhr will be illustrated that the afhr achieves higher resolution effectiveness than the other fuzzy resolution and the proof procedures show the completeness of the afhr