needed reduction and spine strategies for the lambda calculus abstract a redex r in a lambda term m is called needed if in every reduction of m to normal form some residual of r is contracted among others the following results are proved 1 r is needed in m iff r is contracted in the leftmost reduction path of m 2 let r m0 m1 m2 reduce redexes ri mi mi 1 and have the property that i j i rj is needed in mj then r is normalising i e if m0 has a normal form then r is finite and terminates at that normal form 3 neededness is an undecidable property but has several efficiently decidable approximations various versions of the so called spine redexes

order sorted model theory for temporal executable specifications abstract an order sorted temporal programming paradigm is presented it consists of a typed modular declarative language its associated order sorted temporal horn clause logic basis and a model theory generalizing order sorted algebras with predicates to temporal order sorted structures the essence of this generalization is in time dependent interpretation of predicates so that a temporal order sorted model amounts to a sequence of order sorted equational models with predicates one per each state the main advantage of the presented paradigm in comparison with paradigms based on horn clause logic with equality is that it is more expressive particularly so in representing properly state transitions and other event oriented temporal behavioral properties of objects at the same time the generalized paradigm is proved to have the initial model semantics the rules for temporal order sorted deduction are established as an appropriate generalization of the rules for order sorted horn clause logic with equality the initial model is a quotient temporal order sorted structure constructed from the initial temporal order sorted structure and a congruence relation derived from a given set of temporal constraints temporal order sorted model theoretic properties are also naturally established for temporal queries the temporal constraint language has an execution model and it is intended to be a basis for a prototyping tool for complex typed modular software systems

infinitary lambda calculus in a previous paper we have established the theory of transfinite reduction for orthogonal term rewriting systems in this paper we perform the same task for the lambda calculus from the viewpoint of infinitary rewriting the bohm model of the lambda calculus can be seen as an infinitary term model in contrast to term rewriting there are several different possible notions of infinite term which give rise to different bohm like models which embody different notions of lazy or eager computation

a modular order sorted equational generalization algorithm generalization also called anti unification is the dual of unification given terms t and t a generalizer is a term t of which t and t are substitution instances the dual of a most general unifier mgu is that of least general generalizer lgg in this work we extend the known untyped generalization algorithm to first an order sorted typed setting with sorts subsorts and subtype polymorphism second we extend it to work modulo equational theories where function symbols can obey any combination of associativity commutativity and identity axioms including the empty set of such axioms and third to the combination of both which results in a modular order sorted equational generalization algorithm unlike the untyped case there is in general no single lgg in our framework due to order sortedness or to the equational axioms instead there is a finite minimal and complete set of lggs so that any other generalizer has at least one of them as an instance our generalization algorithms are expressed by means of inference systems for which we give proofs of correctness this opens up new applications to partial evaluation program synthesis and theorem proving for typed equational reasoning systems and typed rule based languages such as asf sdf elan obj cafe obj and maude

some new results on easy lambda terms abstract given two closed terms a and b we consider the question whether the equation a b is consistent with the calculus in general the problem is undecidable however if a is a 0 term we can give good sufficient conditions for the consistency of a b this allows us to prove some counterintuitive results such as 1 there is a closed term x which can be consistently equated to every closed term with the exception of the identity 2 there is a closed term which can be consistently equated to every closed normal form but not to the curry fixed point operator y

on the dziok srivastava operator under multivalent analytic functions abstract the aim of this paper is to investigate various properties and characteristics of the dziok srivastava operator introduced in dziok and srivastava j dziok h m srivastava classes of analytic functions associated with the generalized hypergeometric function appl math comput 103 1999 1 13 our paper is motivated essentially by the familiar work liu and srivastava j l liu h m srivastava certain properties of the dziok srivastava operator appl math comput 159 2004 485 493 which has been recently published

rewriting extended regular expressions we concider an extened algebra of regular events languages with intersection besides the usual operations this algebra has the structure of a distributive lattice with monotonic operations the latter property is crucial for some applications we give a new complete horn equational axiomatiztion of the algebra and develop some termrewriting techniques for constructing logical inferences of valid equations

order sorted algebra i equational deduction for multiple inheritance overloading exceptions and partial operations abstract this paper generalizes many sorted algebra msa to order sorted algebra osa by allowing a partial ordering relation on the set of sorts this supports abstract data types with multiple inheritance in roughly the sense of object oriented programming several forms of polymorphism and overloading partial operations as total on equationally defined subsorts exception handling and an operational semantics based on term rewriting we give the basic algebraic constructions for osa including quotient image product and term algebra and we prove their basic properties including quotient homomorphism and initiality theorems the paper s major mathematical results include a notion of osa deduction a completeness theorem for it and an osa birkhoff variety theorem we also develop conditional osa including initiality completeness and mckinsey malcev quasivariety theorems and we reduce osa to conditional msa which allows lifting many known msa results to osa retracts which intuitively are left inverses to subsort inclusions provide relatively inexpensive run time error handling we show that it is safe to add retracts to any osa signature in the sense that it gives rise to a conservative extension a final section compares and contrasts many different approaches to osa this paper also includes several examples demonstrating the flexibility and applicability of osa including some standard benchmarks like stack and list as well as a much more substantial example the number hierarchy from the naturals up to the quaternions

multiplication of fractional calculus operators and boundary value problems involving the euler darboux equation abstract with a view to presenting solutions of various boundary value problems involving the celebrated euler darboux equation the authors consider the multiplication of certain classes of operators of fractional calculus defined in terms of the gaussian hypergeometric function the fractional calculus operators studied here incorporate as their special cases both the riemann liouville and erdelyi kober operators and are appropriately restricted in order to yield explicit solutions of some of the aforementioned boundary value problems in terms of appell functions and kampe de feriet functions of two variables

highlights in infinitary rewriting and lambda calculus we present some highlights from the emerging theory of infinitary rewriting both for first order term rewriting systems and l calculus in the first section we introduce the framework of infinitary rewriting for first order rewrite systems so without bound variables we present a recent observation concerning the continuity of infinitary rewriting in the second section we present an excursion to the infinitary l calculus after the main definitions we mention a recent observation about infinite looping l terms that is terms that reduce in one step to themselves next we describe the fundamental trichotomy in the semantics of l calculus bohm trees levy longo trees and berarducci trees we conclude with a short description of a new refinement of bohm tree semantics called clocked semantics

programming in metric temporal logic abstract we present a fragment of metric temporal logic called bounded universal horn formulae as a theoretical basis for temporal reasoning in logic programming we characterize its semantics in terms of fixed points and canonical models and present an efficient proof method as operational semantics based on sld resolution with constraints although the complexity of real time logics is very high in general the validity problem for most of them is 1 l complete already for propositional fragments in case of dense time structures we show that the class of bounded universal horn formulae admits complete and efficient proof methods exploiting uniform proofs and linear time complexity of basic steps of the proof method the results obtained heavily rely on the fragment investigated and make it necessary to establish some basic results like compactness and approximation of the least model by at most steps of the corresponding fixed point operator directly without recourse to standard methods in dense case the fragment itself is sufficiently expressive for a variety of applications ranging from real time systems temporal deductive data bases and sequence evaluation purposes we show that the fragment is the greatest of the metric temporal logic in discrete and dense case having the properties classically desired for logic programming languages

concerning the semantic consequence relation in first order temporal logic in this paper we consider the first order temporal logic with linear and discrete time we prove that the set of tautologies of this logic is not arithmetical i e it is neither 0n nor 0n for any natural number n thus we show that there is no finitistic and complete axiomatization of the considered logic

some classes of analytic functions involving noor integral operator the object of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions defined by using the noor integral operator the integral preserving properties in connection with the operator are also considered relevant connections of the results presented here with those obtained in earlier works are pointed out

applications of infinitary lambda calculus we present an introduction to infinitary lambda calculus highlighting its main properties subsequently we give three applications of infinitary lambda calculus the first addresses the non definability of surjective pairing which was shown by the first author not to be definable in lambda calculus we show how this result follows easily as an application of berry s sequentiality theorem which itself can be proved in the setting of infinitary lambda calculus the second pertains to the notion of relative recursiveness of number theoretic functions the third application concerns an explanation of counterexamples to confluence of lambda calculus extended with non left linear reduction rules adding non left linear reduction rules such as dxx x or the reduction rules for surjective pairing to the lambda calculus yields non confluence as proved by the second author we discuss how an extension to the infinitary lambda calculus where bohm trees can be directly manipulated as infinite terms yields a more simple and intuitive explanation of the correctness of these church rosser counterexamples

properties and characteristics of the srivastava khairnar more integral operator abstract in the present paper we derive various properties and characteristics of the srivastava khairnar more integral operator such results as inclusion relationships integral preserving properties inequality properties convolution properties subordination and superordination properties and sandwich type results are obtained relevant connections of the results presented here with those obtained in earlier works are also pointed out

a class of bounded functions a database language and an extended lambda calculus abstract we develop an approach of partial computations for the lambda calculus it produces a class of bounded functions i e the co domains are finite while the domains are possibly infinite including self applicable functions we show that the bounded functions are recursive and have to be represented as lambda terms without head normal form in the lambda calculus in parallel we develop a language independently from the lambda calculus it also represents the class of bounded functions and therefore can produce whatever a turing machine produces provided that computation has finite time and space we call such a language a database language because we can use the language to construct and query business objects in database practice with the bounded functions we are able to extend the lambda calculus to effectively reduce terms having weak head normal form in a manner similar to how the standard lambda calculus reduces terms that have normal form

levels of undecidability in rewriting undecidability of various properties of first order term rewriting systems is well known an undecidable property can be classified by the complexity of the formula defining it this classification gives rise to a hierarchy of distinct levels of undecidability starting from the arithmetical hierarchy classifying properties using first order arithmetical formulas and continuing into the analytic hierarchy where quantification over function variables is allowed in this paper we give an overview of how the main properties of first order term rewriting systems are classified in these hierarchies we consider properties related to normalization strong normalization weak normalization and dependency problems and properties related to confluence confluence local confluence and the unique normal form property for all of these we distinguish between the single term version and the uniform version where appropriate we also distinguish between ground and open terms most uniform properties are p 2 0 complete the particular problem of local confluence turns out to be p 2 0 complete for ground terms but only p 2 0 complete and thereby recursively enumerable for open terms the most surprising result concerns dependency pair problems without minimality flag we prove this problem to be p 1 1 complete hence not in the arithmetical hierarchy but properly in the analytic hierarchy some of our results are new or have appeared in our earlier publications others are based on folklore constructions and are included for completeness as their precise classifications have hardly been noticed previously

some further properties of a linear operator associated with the λ generalized hurwitz lerch zeta function related to the class of meromorphically univalent functions in this sequel to the recent work see srivastava 2015 we investigate some further properties of a linear operator associated with srivastava s generalized hurwitz lerch zeta function which are related to a certain class of meromorphically univalent functions in the punctured unit disk defined here by means of the hadamard product or convolution we also give several interesting corollaries and consequences of the main results presented in this paper

principles of proof scores in cafeobj this paper describes the theoretical principles of a verification method with proof scores in the cafeobj algebraic specification language the verification method focuses on specifications with conditional equations and realizes systematic theorem proving or interactive verification the method is explained using a simple but instructive example and the necessary theoretical foundations which justify every step of the verification are described with precise mathematical definitions some important theorems that result from the definitions are also presented

some applications of differential subordination and the dziok srivastava convolution operator abstract by making use of the principle of differential subordination and the dziok srivastava convolution operator we introduce and investigate three interesting subclasses of analytic and univalent functions in the open unit disk we obtain their inclusion relationships and also show that these classes are closed under convolution with convex functions the results presented in this paper provide generalizations of several recent works by for example ozkan and altintas 2006 16 trojnar spelina 2008 30 and many other authors

multimodal logic programming using equational and order sorted logic in previous work 2 we proposed a method for automated modal theorem proving based on algebraic concepts and equational techniques basically it uses the translation of modal logic into a specially tailored multi sorted logic called path logic in this paper we extend the method for multi modal logic and apply it to multi modal logic programming the multi modal systems we consider are arbitrary mixing of first order modal systems of type kd kt kd4 or kt4 with interaction axioms of the form ia ja roughly with each modal subsystem is associated a sort in path logic and a specific set of equations and the interaction axioms are captured by the order relation between sorts hence again all the modal logical rules are coded in the unification algorithm if one considers horn clauses in the usual sense we get a logic programming system pathlog for which standard theoretical results apply in pathlog one can either write programs directly in the language of path logic or in various multi modal logics the modal formulas being automatically translated and put in clausal form for instance we obtain as a particular case a system for temporal logic programming which subsumes templog of 1 and whose completeness results immediately from our general theorems

strict coherence of conditional rewriting modulo axioms conditional rewriting modulo axioms with rich types makes specifications and declarative programs very expressive and succinct and is used in all well known rule based languages however the current foundations of rewriting modulo axioms have focused for the most part on the unconditional and untyped case the main purpose of this work is to generalize the foundations of rewriting modulo axioms to the conditional order sorted case a related goal is to simplify such foundations in particular even in the unconditional case the notion of strict coherence proposed here makes rewriting modulo axioms simpler and easier to understand properties of strictly coherent conditional theories like operational equi termination of the r b and r b relations and general conditions for the conditional churchrosser property modulo b are also studied

specification and proof in membership equational logic this paper is part of a long term effort to increase expressiveness of algebraic specification languages while at the same time having a simple semantic basis on which efficient execution by rewriting and powerful theorem proving tools can be based in particular our rewriting techniques provide semantic foundations for maude s functional sublanguage where they have been efficiently implemented

relating casl with other specification languages the institution level in this work we investigate various specification languages and their relation to casl the recently developed common algebraic specification language in particular we consider the languages larch obj3 and functional cafeobj act one asf and hep theories as well as various sublanguages of casl all these languages are translated to an appropriate sublanguage of casl the translation mainly concerns the level of specification in the small the logics underlying the languages are formalized as institutions and representations among the institutions are developed however it is also considered how these translations interact with specification in the large thus we obtain on the one hand translations of any of the above mentioned specification languages to an appropriate sublanguage of casl this allows us to take libraries and case studies that have been developed for other languages and re use them in casl on the other hand we set up institution representations going from the casl institution and some of its subinstitutions to simpler subinstitutions given a theorem proving tool for such a simpler subinstitution with the help of a representation it can also be used for a more complex institution thus first order theorem provers and conditional term rewriting tools become usable for casl

on proof normalization in linear logic abstract we present a proof theoretic foundation for automated deduction in linear logic at first we systematically study the permutability properties of the inference rules in this logical framework and exploit these to introduce an appropriate notion of forward and backward movement of an inference in a proof then we discuss the naturally arising question of the redundancy reduction and investigate the possibilities of proof normalization which depend on the proof search strategy and the fragment we consider thus we can define the concept of normal proof that might be the basis of works about automatic proof construction and design of logic programming languages based on linear logic

some inclusion properties of a certain family of integral operators abstract the authors introduce several new subclasses of analytic functions which are defined by means of a general integral operator i and investigate various inclusion properties of these subclasses many interesting applications involving these and other families of integral operators are also considered

on analytic functions with generalized bounded mocanu variation in this paper we introduce and study a class of normalized analytic functions defined in the open unit disc this class contains several known classes of analytic functions such as those of functions with bounded boundary rotation bounded radius rotation and bounded mocanu variation it also generalizes the concept of bazilevic functions in some sense inclusion results arclength problem coefficient bounds and distortion results with some other properties of this class are investigated

a tableau like proof procedure for normal modal logics abstract in this paper a new proof procedure for some propositional and first order normal modal logics is given it combines a tableau like approach and a resolution like inference completeness and decidability for some propositional logics are proved an extension for the first order case is presented

generalizations of multivalent mocanu functions in the paper we generalize the class of multivalent mocanu functions the main object is to obtain characterizations and inclusion properties for defined classes of functions some applications of the main results to classes defined by the srivastava wright operator are also considered

a causal semantics for ccs via rewriting logic we consider two operational semantics for ccs defined in the literature the first exploits proved transition systems pts and the second rewriting logic rl we show that the interleaving interpretation of both semantics agree in that they define the same transitions and exhibit the same non deterministic structure in addition we study causality in ccs computations we recall its treatment via pts exhibiting the notion of causality presented in the literature and we show how to recast it in the rl semantics via suitable axioms also in this case the two semantics agree

unions of non disjoint theories and combinations of satisfiability procedures in this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability we describe a general combination method which given a procedure that decides constraint satisfiability with respect to a constraint theory t1 and one that decides constraint satisfiability with respect to a constraint theory t2 produces a procedure that semi decides constraint satisfiability with respect to the union of t1 and t2 we provide a number of model theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete with special emphasis on the case in which the signatures of the component theories are non disjoint we also describe some general classes of theories to which our combination results apply and relate our approach to some of the existing combination methods in the field

semantics of temporal classes a model theory of a typed declarative temporal object oriented language system is presented the declarative nature of the language makes it very different from the dominating procedural strongly typed object oriented programming languages in this declarative system methods are specified in a high level temporal constraint language two fundamental properties of these constraints are that they have an execution model and algebraic semantics the model theory is based on temporal order sorted algebras with predicates a variety of orderings are explored in order to represent various types of inheritance as well as the subtyping discipline temporal classes are viewed as temporal theories and some inheritance relationships as morphisms of temporal theories a model of a temporal class is a temporal order sorted structure with predicates which satisfies a set of temporal constraints specified in that class morphisms of those models are naturally required to preserve type coercions a distinguished model of a temporal theory is constructed as a colimit of a suitably defined functor this colimit construction reflects the temporal nature of the paradigm and generalizes the classical initial algebra semantics in contradistinction to major difficulties in developing a model theory for full fledged typed procedural object oriented languages this paper shows that such a task becomes possible for a suitably defined declarative object oriented language this in particular leads to model theoretic results on the preservation of the behavioral properties in the inheritance hierarchies

nonclausal deduction in first order temporal logic this paper presents a proof system for first order temporal logic the system extends the nonclausal resolution method for ordinary first order logic with equality to handle quantifiers and temporal operators soundness and completeness issues are considered the use of the system for verifying concurrent programs is discussed and variants of the system for other modal logics are also described

infinitary lambda calculus and discrimination of berarducci trees we propose an extension of lambda calculus for which the berarducci trees equality coincides with observational equivalence when we observe rootstable or rootactive behavior of terms in one direction the proof is an adaptation of the classical bohm out technique in the other direction the proof is based on confluence for strongly converging reductions in this extension

some inclusion relationships associated with dziok srivastava operator in this paper we introduce and study some new subclasses of p valent starlike convex close to convex and quasi convex functions defined by dziok srivastava operator inclusion relationships are established and integral operator of functions in these subclasses is discussed

infinitary combinatory reduction systems we define infinitary combinatory reduction systems icrss thus providing the first notion of infinitary higher order rewriting the systems defined are sufficiently general that ordinary infinitary term rewriting and infinitary l calculus are special cases furthermore we generalise a number of known results from first order infinitary rewriting and infinitary l calculus to icrss in particular for fully extended left linear icrss we prove the well known compression property and for orthogonal icrss we prove that 1 if a set of redexes u has a complete development then all complete developments of u end in the same term and that 2 any tiling diagram involving strongly convergent reductions s and t can be completed iff at least one of s t and t s is strongly convergent we also prove an ancillary result of independent interest a set of redexes in an orthogonal icrs has a complete development iff the set has the so called finite jumps property

lambda calculus with explicit recursion this paper is concerned with the study of calculus with explicit recursion namely of cyclic graphs the starting point is to treat a graph as a system of recursion equations involving terms and to manipulate such systems in an unrestricted manner using equational logic just as is possible for first order term rewriting surprisingly now the confluence property breaks down in an essential way confluence can be restored by introducing a restraining mechanism on the substitution operation this leads to a family of graph calculi which can be seen as an extension of the family of calculi calculi with explicit substitution while the calculi treat the let construct as a first class citizen our calculi support the letrec a feature that is essential to reason about time and space behavior of functional languages and also about compilation and optimizations of programs

on some implication type results involving generalized bounded mocanu variations this paper is the study of certain implication type results involving functions related to generalized bounded mocanu variations basic properties involving generalized bernardi integral transform inclusion results and a sharp radius problem are investigated for such classes many interesting implications are observed as special cases of our results

order sorted inductive types abstract system f is an extension of system f with subtyping and bounded quantification order sorted algebra is an extension of many sorted algebra with overloading and subtyping we combine both formalisms to obtain if a higher order typed calculus with subtyping bounded quantification and order sorted inductive types i e data types with built in subtyping and overloading moreover we show that if enjoys important meta theoretic properties including confluence strong normalization subject reduction and decidability of type checking

generalized hypergeometric functions associated with k uniformly convex functions abstract for a certain linear operator which is defined by means of the hadamard product or convolution with a generalized hypergeometric function the authors aim at investigating various mapping and inclusion properties involving such subclasses of analytic and univalent functions as for example k uniformly convex functions and k starlike functions relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out

inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators abstract by making use of a general linear operator i p a c the authors introduce several new subclasses of multivalent functions and investigate various inclusion relationships and argument properties associated with these subclasses some interesting applications involving such and other families of linear operators are also considered the results presented here include a number of known results as their special cases

on sets of solutions to combinator equations abstract we show that every r e set of combinators closed under conversion is the set of solutions to a pattern matching problem

transfinite reductions in orthogonal term rewriting systems strongly convergent reduction is the fundamental notion of reduction in infinitary orthogonal term rewriting systems otrss for these we prove the transfinite parallel moves lemma and the compressing lemma strongness is necessary as shown by counterexamples normal forms which we allow to be infinite are unique in contrast to normal forms strongly converging fair reductions result in normal forms

some subclasses of multivalent functions involving a certain linear operator the authors investigate various inclusion and other properties of several subclasses of the class ap of normalized p valent analytic functions in the open unit disk which are defined here by means of a certain linear operator problems involving generalized neighborhoods of analytic functions in the class ap are investigated finally some applications of fractional calculus operators are considered

lazy productivity via termination abstract we present a procedure for transforming strongly sequential constructor based term rewriting systems trss into context sensitive trss in such a way that productivity of the input system is equivalent to termination of the output system thereby automated termination provers become available for proving productivity a trs is called productive if all its finite ground terms are constructor normalizing and all inductive constructor paths through the resulting possibly non wellfounded constructor normal form are finite to our knowledge this is the first complete transformation from productivity to termination the transformation proceeds in two steps i the strongly sequential trs is converted into a shallow trs where patterns do not have nested constructors ii the shallow trs is transformed into a context sensitive trs where rewriting below constructors and in arguments not consumed from is disallowed furthermore we show how lazy evaluation can be encoded by strong sequentiality thus extending our transformation to e g haskell programs finally we present a simple but fruitful extension of matrix interpretations to make them applicable for proving termination of context sensitive trss

criteria for univalence of the dziok srivastava and the srivastava wright operators in the class a abstract in the geometric function theory gft much attention is paid to various linear integral operators mapping the class s of the univalent functions and its subclasses into themselves in 12 13 hohlov obtained sufficient conditions that guarantee such mappings for the operator defined by means of hadamard product with the gauss hypergeometric function in our earlier papers as 20 19 17 18 etc we extended his method to the operators of the generalized fractional calculus gfc 16 these operators have product functions of the forms m 1 f m and m 1 m and integral representations by means of the meijer g and fox h functions here we propose sufficient conditions that guarantee mapping of the univalent respectively of the convex functions into univalent functions in the case of the celebrated dziok srivastava operator 8 j dziok h m srivastava classes of analytic functions associated with the generalized hypergeometric function appl math comput 103 no 1 1999 pp 1 13 defined as a hadamard product with an arbitrary generalized hypergeometric function p f q similar conditions are suggested also for its extension involving the wright p q function and called the srivastava wright operator srivastava 36 since the discussed operators include the above mentioned gfc operators and many their particular cases operators of the classical fc from the results proposed here one can derive univalence criteria for many named operators in the gft as the operators of hohlov carlson and shaffer saigo libera bernardi erdelyi kober etc by giving particular values to the orders p q 1 of the generalized hypergeometric functions and to their parameters

certain properties of the dziok srivastava operator the main object of the present paper is to investigate several interesting properties and characteristics of a linear operator h p q s a 1 which was recently introduced and studied in a series of papers by dziok and srivastava appl math comput 103 1999 1 13 adv stud contemp math 5 2002 115 125 integral transform spec funct 14 2003 7 18 the various properties and characteristics of the linear operator h p q s a 1 which are considered in this paper are associated with for example the principle of differential subordination between analytic functions and a certain one parameter family of integral operators

partial derivatives of regular expressions and finite automaton constructions we introduce a notion of a partial derivative of a regular expression it is a generalization to the non deterministic case of the known notion of a derivative invented by brzozowski we give a constructive definition of partial derivatives study their properties and employ them to develop a new algorithm for turning regular expressions into relatively small nfa and to provide certain improvements to brzozowski s algorithm constructing dfa we report on a prototype implementation of our algorithm constructing nfa and present some examples

on certain analytic functions associated with ruscheweyh derivatives and bounded mocanu variation using ruscheweyh derivative and convolution operator we introduce a new subclass of analytic functions defined in the unit disc some inclusion results a radius problem and some other interesting properties of this class are investigated

fuzzy terms in this paper we will show how purely categorical constructions of terms are advantageous when investigating situations concerning uncertainty more specifically where uncertainty comes from and how uncertainty is integrated when dealing with terms over selected signatures there are basically two ways of invoking uncertainty for terms on one hand we may proceed by building composed monads where uncertainty is provided by some suitable monad composed with the traditional term monad on the other hand we can provide a strictly formal basis for term monads being created over categories themselves carrying uncertainty this is the distinction between computing with fuzzy and fuzzy computing and the fundamental question raised by these constructions is where uncertainty resides in language constructions for logic this paper also shows how the notion of signature often needs to be expanded to levels of signatures in particular when dealing with type constructors such levels allow us to strictly delineate e g primitive operations type terms and value level terms levels of signature will in this paper be exemplified by the construction of the signature of simply typed lambda calculus

multimodal logic programming we give a framework for developing the least model semantics fixpoint semantics and sld resolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality i e x y ri x y and some classical first order horn clauses our approach is direct and no special restriction on occurrences of i and i is required we apply our framework for a large class of basic serial multimodal logics which are parametefized by an arbitrary combination of generalized versions of axioms t b 4 5 in the form e g 4 i j k and i i j another part of the work is devoted to programming in multimodal logics intended for reasoning about multidegree belief for use in distributed systems of belief or for reasoning about epistemic states of agents in multiagent systems for that we also use the framework and although these latter logics belong to the mentioned class of basic serial multimodal logics the special sld resolution calculi proposed for them are more efficient

neighborhoods of a certain family of multivalent functions with negative coefficients abstract by making use of the familiar concept of neighborhoods of analytic and p valent functions the authors prove coefficient bounds and distortion inequalities and associated inclusion relations for the n neighborhoods of a family of multivalent functions with negative coefficients which is defined by means of a certain nonhomogeneous cauchy euler differential equation relevant connections of the various function classes investigated in this paper with those considered by earlier workers on the subject are also mentioned

classes of multivalent analytic functions involving the dziok srivastava operator the object of the present paper is to investigate some inclusion relationships and a number of other useful properties of several subclasses of multivalent analytic functions which are defined here by using the dziok srivastava operator relevant connections of the results presented here with those obtained in earlier works are pointed out

non existent statman s double fixed point combinator does not exist indeed we give a negative answer to a problem of r statman concerning the existence in the lambda calculus of a fixed point combinatorysuch thaty si yholds

the computational complexity of the satisfiability of modal horn clauses for modal propositional logics abstract this paper presents complexity results about the satisfiability of modal horn clauses for several modal propositional logics almost all these results are negative in the sense that restricting the input formula to modal horn clauses does not decrease the inherent complexity of the satisfiability problem we first show that when restricted to modal horn clauses the satisfiability problem for any modal logic clauses as well as the satisfiability of unrestricted formulas for any of k t b ans s4 is pspace complete this result refutes the expectation farinas del cerro and penttonen 1987 of getting a polynomial time algorithm for the satisfiability of modal horn clauses for these logics as long as p pspace next we consider s4 3 and extensions of k5 including k5 kd5 k45 kd45 and s5 the satisfiability problem for each of which in general is known to be np complete and show that for each extension of k5 a polynomial time algorithm for the satisfiability of modal horn clauses can be obtained but for s4 3 together with some linear tense logics closely related to s4 3 like cl sl and pl the satisfiability of modal horn clauses still remains np complete

univalent solutions of briot bouquet differential equations let and be complex numbers and let h z be regular in the unit disc u in this article the authors study the briot bouquet differential equation q z frac zq z beta q z gamma h z sufficient conditions are obtained for both the regularity and univalency of the solution in u in addition applications of these results to differential subordinations integral operators and univalent functions are given

some classes of p valent analytic functions defined by certain integral operator let a p p n be the class of functions f z z p a p 1z p 1 analytic in the open unit disc e for n 0 1 2 n p a certain integral operator i n p 1 a p a p is defined as i n p 1f f 1 n p 1 f such that f 1 n p 1 f n p 1 z z p1 z where f n p 1 z z p 1 z n p and denotes convolution or hadamard product using this integral operator a new subclass s n p a of a p 0 a

on the convex combination of the dziok srivastava operator in the paper we obtain the extreme points of some class defined by the dziok srivastava linear operator by using the krein milman theorem some extremal problems in the class are determined

on integral operators abstract let fn z z 1 z n 1 n no and f 1 n be defined such that f n f 1 n z 1 z where denotes convolution hadamard product let f be analytic in the unit disc e we define a new operator inf f 1 n f which is analogous to one defined by ruscheweyh using this operator the classes m n are defined a function f analytic in e is in m n if and only if inf is close to convex the properties of f m n are discussed in some detail it is shown that m n m n 1 for n no and for n 0 1 m n consists entirely of univalent functions closure properties of some integral operators defined on m n are also given

towards a general theory of action and time abstract a formalism for reasoning about actions is proposed that is based on a temporal logic it allows a much wider range of actions to be described than with previous approaches such as the situation calculus this formalism is then used to characterize the different types of events processes actions and properties that can be described in simple english sentences in addressing this problem we consider actions that involve non activity as well as actions that can only be defined in terms of the beliefs and intentions of the actors finally a framework for planning in a dynamic world with external events and multiple agents is suggested

representing scope in intuitionistic deductions abstract intuitionistic proofs can be segmented into scopes which describe when assumptions can be used in standard descriptions of intuitionistic logic these scopes occupy contiguous regions of proofs this leads to an explosion in the search space for automated deduction because of the difficulty of planning to apply a rule inside a particular scoped region of the proof this paper investigates an alternative representation which assigns scope explicitly to formulas and which is inspired in part by semantics based translation methods for modal deduction this calculus is simple and is justified by direct proof theoretic arguments that transform proofs in the calculus so that scopes match standard descriptions a herbrand theorem established straightforwardly lifts this calculus to incorporate unification the resulting system has no impermutabilities whatsoever rules of inference may be used equivalently anywhere in the proof nevertheless a natural specification describes how terms are to be extracted from its deductions

modal resolution in clausal form abstract this paper concerns the question of automated deduction methods for modal logic a method called modal resolution and inspired by robinson s resolution method for classical logics is presented for the system k and then extended to q t s4 epistemic logic and s5 a completeness proof technique based on a variant of the tableau method for formulas in some clausal form is presented and applied to these systems an algorithm implementing the method and including a deletion strategy using a subsumption relation is established

classes of analytic functions associated with the generalized hypergeometric function using the generalized hypergeometric function we introduce and study a class of analytic functions with negative coefficients coefficients estimates distortion theorems extreme points and the radii of convexity and starlikeness for this class are given relevant connections of these results with those in several earlier investigations are indicated

on subordinations for certain analytic functions associated with noor integral operator by making use of the method of differential subordination we investigate several interesting properties of the noor integral operator

a class of distortion theorems involving certain operators of fractional calculus abstract the object of the present paper is to investigate a general class of fractional integral operators involving the gauss hypergeometric function several interesting distortion theorems for various subclasses of analytic and univalent functions are proved in terms of these operators of fractional calculus some special cases of the results presented here are also indicated

conditional rewriting logic as a unified model of concurrency abstract rewriting with conditional rewrite rules modulo a set e of structural axioms provides a general framework for unifying a wide variety of models of concurrency concurrent rewriting coincides with logical deduction in conditional rewriting logic a logic of actions whose models are concurrent systems this logic is sound and complete and has initial models in addition to general models interpreted as concurrent systems which provide a more operational style of semantics more restricted semantics with an incresingly denotational flavor such as preorder poset cpo and standard algebraic models appear as special cases of the model theory this permits dealing with operational and denotational issues within the same model theory and logic a programming language called maude whose modules are rewriting logic theories is defined and given denotational and operational semantics maude provides a simple unification of concurrent programming with functional and object oriented programming and supports high level declarative programming of concurrent systems

the power of temporal proofs abstract some methods for reasoning about concurrent programs and hardware devices have been based on proof systems for temporal logic unfortunately all effective proof systems for temporal logic are incomplete for the standard semantics in the sense that some formulas hold in every intended model but cannot be proved we evaluate and compare the power of several proof systems for temporal logic specifically we relate temporal systems to classical systems with explicit time parameters a typical temporal system turns out to be incomplete in a strong sense we exhibit a short valid formula it fails to prove we suggest the addition of new rules to define auxiliary predicates with these rules we obtain nonstandard soundness and completeness results in particular one of the simple temporal systems we describe is as powerful as peano arithmetic

on some applications of the dziok srivastava operator abstract carlson and shaffer b c carlson d b shaffer starlike and prestarlike hypergeometric functions siam j math anal 15 1984 737 745 have introduced a linear operator associated with the gaussian hypergeometric function which has been generalized by dziok and srivastava j dziok h m srivastava classes of analytic functions associated with the generalized hypergeometric function appl math comput 103 1999 1 13 certain classes of analytic functions defined by means of those operators have been considered in j dziok h m srivastava certain subclasses of analytic functions associated with the generalized hypergeometric function integral transform spec funct 14 2003 7 18 j dziok h m srivastava some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function adv stud contemp math 5 2 2002 115 125 and recently in j dziok on some applications of the briot bouquet differential subordination j math anal appl 328 2007 295 301 j dziok some relations including various linear operators demonstratio math xl 2007 77 84 j l liu h m srivastava certain properties of the dziok srivastava operator appl math comput 159 2004 485 493 in the present paper new results for a familiar class of multivalent functions have been obtained we have used the methods of differential subordination and the properties of hadamard product

productivity of stream definitions we give an algorithm for deciding productivity of a large and natural class of recursive stream definitions a stream definition is called productive if it can be evaluated continually in such a way that a uniquely determined stream in constructor normal form is obtained as the limit whereas productivity is undecidable for stream definitions in general we show that it can be decided for pure stream definitions for every pure stream definition the process of its evaluation can be modelled by the dataflow of abstract stream elements called pebbles in a finite pebbleflow net work and the production of a pebbleflow net associated with a pure stream definition that is the amount of pebbles the net is able to produce at its output port can be calculated by reducing nets to trivial nets

applications of multivalent prestarlike functions in the paper we introduce general classes of multivalent analytic functions defined by the subordination in particular we define the class of multivalent prestarlike functions by using the ruscheweyh s duality theory we investigate convolution properties related to multivalent prestarlike functions and various inclusion relationships between defined classes of functions some applications involving well known classes of functions defined by linear operators are also considered