fuzzy non continuous mappings and fuzzy pre semi separation axioms the aim of the paper is mainly to introduce and study fuzzy pre semi open mapping fuzzy pre semi irresolute mapping fuzzy pre semi separation axioms and fuzzy pre semi connectedness in fuzzy topological spaces

q convergence of nets and weak separation axioms in fuzzy lattices abstract in this paper we introduce the concept of q remote neighborhood and establish the q convergence theory of nets in fuzzy lattices next we introduce the st i i 1 0 1 2 separation axioms in fuzzy lattices and discuss some of their characterizations finally we introduce and study s irresolute order homomorphism and s homeomorphism discuss the application of q convergence of nets and show that the st i i 1 0 1 2 separability is preserved under s homeomorphism

optimal compression of propositional horn knowledge bases complexity and approximation abstract horn formulae play a prominent role in artificial intelligence and logic programming in this paper we investigate the problem of optimal compression of propositional horn production rule knowledge bases the standard approach to this problem consisting in the removal of redundant rules from a knowledge base leads to an irredundant but not necessarily optimal knowledge base we prove here that the number of rules in any irredundant horn knowledge base involving n propositional variables is at most n 1 times the minimum possible number of rules therefore the quadratic time transformation of an arbitrary horn production rule base to an equivalent irredundant and prime one presented in 9 provides a reasonable approximation algorithm in order to formalize the optimal compression problem we define a boolean function of a knowledge base as being the function whose set of true points is the set of models of the knowledge base in this way the optimal compression of production rule knowledge bases becomes a problem of boolean function minimization in this paper we prove that the minimization of horn functions i e boolean functions associated to horn knowledge bases is np complete

conditional independence in propositional logic independence the study of what is relevant to a given problem of reasoning is an important ai topic in this paper we investigate several notions of conditional independence in propositional logic darwiche and pearl s conditional independence and some more restricted forms of it many characterizations and properties of these independence relations are provided we show them related to many other notions of independence pointed out so far in the literature mainly formula variable independence irrelevance and novelty under various forms separability interactivity we identify the computational complexity of conditional independence and of all these related independence relations

lost in translation language independence in propositional logic application to belief change while propositional logic is widely used as a representation framework for many ai applications the concept of language independence in the propositional setting has not received much attention so far in this paper we define language independence for a propositional operator as robustness w r t symbol translation we motivate the need to focus on symbol translations of restricted types introduce and study several families of translations of interest and provide a number of characterization results we also identify the computational complexity of recognizing symbol translations from those families then we investigate the robustness of belief merging belief revision and belief update operators w r t translations of different types it turns out that some rational merging revision update operators are not guaranteed to offer the most basic yet non trivial form of language independence

a theory of diagnosis from first principles suppose one is given a description of a system together with an observation of the system s behaviour which conflicts with the way the system is meant to behave the diagnostic problem is to determine those components of the system which when assumed to be functioning abnormally will explain the discrepancy between the observed and correct system behaviour we propose a general theory for this problem the theory requires only that the system be described in a suitable logic moreover there are many such suitable logics e g first order temporal dynamic etc as a result the theory accommodates diagnostic reasoning in a wide variety of practical settings including digital and analogue circuits medicine and database updates the theory leads to an algorithm for computing all diagnoses and to various results concerning principles of measurement for discriminating among competing diagnoses finally the theory reveals close connections between diagnostic reasoning and nonmonotonic reasoning

on closedness of the attainable set of a delay system multicontrol case a control delay system with general delays is considered a checkable criterion of closedness of the attainable set in the space w 1 2 is derived the criterion uses the transfer matrix of the system and is an extension of the result of bartosiewicz 2 to the multicontrol case

functional dependencies in horn theories abstract this paper studies functional dependencies in horn theories both when the theory is represented by its clausal form and when it is defined as the horn envelope of a set of models we provide polynomial algorithms for the recognition of whether a given functional dependency holds in a given horn theory as well as polynomial algorithms for the generation of some representative sets of functional dependencies we show that some problems of inferring functional dependencies e g constructing an irredundant fd cover are computationally difficult we also study the structure of functional dependencies that hold in a horn theory showing that every such functional dependency is in fact a single positive term boolean function and prove that for any horn theory the set of its minimal functional dependencies is quasi acyclic finally we consider the problem of condensing a horn theory prove that any horn theory has a unique condensation and develop an efficient polynomial algorithm for condensing horn theories

reasoning with models we develop a model based approach to reasoning in which the knowledge base is represented as a set of models satisfying assignments rather than a logical formula and the set of queries is restricted we show that for every propositional knowledge base kb there exists a set of characteristic models with the property that a query is true in kb if and only if it is satisfied by the models in this set we characterize a set of functions for which the model based representation is compact and provides efficient reasoning these include cases where the formula based representation does not support efficient reasoning in addition we consider the model based approach to abductive reasoning and show that for any propositional kb reasoning with its model based representation yields an abductive explanation in time that is polynomial in its size some of our technical results make use of the monotone theory a new characterization of boolean functions recently introduced the notion of restricted queries is inherent in our approach this is a wide class of queries for which reasoning is efficient and exact even when the model based representation kb provides only an approximate representation of the domain in question moreover we show that the theory developed here generalizes the model based approach to reasoning with horn expressions and captures even the notion of reasoning with horn approximations

semi interior and semi closure of a fuzzy set on definit le semi interieur et la semi fermeture d un ensemble flou d une facon semblable a celle utilisee dans les espaces topologiques ordinaires

irresolute and lmost open functions between fuzzy topological spaces abstract the aim of this paper is to introduce and characterize the concept of fuzzy irresolute functions which is strictly stronger than the concept of fuzzy semi continuous functions and independent of the concept of fuzzy continuous functions the independence of the two definitions of fuzzy almost open functions as introduced in 5 and 3 and some of their characterizations are also established

on strongest neccessary and weakest sufficient conditions abstract given a propositional theory t and a proposition q a sufficient condition of q is one that will make q true under t and a necessary condition of q is one that has to be true for q to be true under t in this paper we propose a notion of strongest necessary and weakest sufficient conditions intuitively the strongest necessary condition of a proposition is the most general consequence that we can deduce from the proposition under the given theory and the weakest sufficient condition is the most general abduction that we can make from the proposition under the given theory we show that these two conditions are dual ones and can be naturally extended to arbitrary formulas we investigate some computational properties of these two conditions and discuss some of their potential applications

on functional dependencies in q horn theories this paper studies functional dependencies in q horn theories and discusses their use in knowledge condensation we introduce compact model based representations of q horn theories analyze the structure of functional dependencies in q horn theories and show that every minimal functional dependency in a q horn theory can be expressed either by a single term or by a single clause we also prove that the set of all minimal functional dependencies in is quasi acyclic we then develop polynomial time algorithms for recognizing whether a given functional dependency holds in a q horn theory which is represented either by a q horn cnf or as the q horn envelope of a set of models finally we show that every q horn theory has a unique condensation and can be condensed in polynomial time

fuzzy weak semicontinuity abstract in this paper we introduce the fuzzy weakly semicontinuous mapping which is the weaker form of both fuzzy semicontinuous and fuzzy almost continuous mappings in fuzzy topological spaces however fuzzy weakly semicontinuous mapping and fuzzy weakly continuous mapping are independent notions then we discuss some characteristic properties of fuzzy semicontinuous fuzzy semiopen fuzzy semiclosed and fuzzy pre semi open mappings

on propositional definability in standard propositional logic logical definability is the ability to derive the truth value of some propositional symbols given a propositional formula and the truth values of some propositional symbols although appearing more or less informally in various ai settings a computation oriented investigation of the notion is still lacking and this paper aims at filling the gap after recalling the two definitions of definability which are equivalent in standard propositional logic while based on different intuitions and defining a number of related notions we give several characterization results and many complexity results for definability we also show close connections with hypothesis discriminability and with reasoning about action and change

an equivalence between relational database dependencies and a fragment of propositional logic it is known that there is an eqmvalence between functional dependencies m a relatmonal database and a certain fragment of proposmonal logic thins eqmvalence is extended to include both functional and multivalued dependencmes thus for each dependency there is a corresponding statement m proposmonal logic it ms then shown that a dependency funcuonal or multivalued is a consequence of a set of dependencies ff and only ff the corresponding proposiuonal statement s a consequence of the corresponding set of proposmonal statements examples are given to show that these techniques are valuable mn provmdmg much shorter proofs of theorems about dependencies than have been obtained by more tradmonal means it is shown that this eqmvalence cannot be extended to include either join dependencies or embedded multmvalued dependencies

a criterion of closedness of an attainable set of a delay system this paper deals with the problem of closedness of an attainable set of a delay system in the state space w21 we give a necessary and sufficient condition of closedness expressed in terms of the transfer matrix of the system

on controllability and observability of time delay systems this paper deals with controllability and observability properties of time delay systems in the state space r n times l p in particular we prove the equivalence of spectral controllability and approximate null controllability moreover it is shown that the necessary condition for approximate f controllability obtained recently by manitius is also sufficient and a verifiable and matrix type criterion for f controllability is derived for systems with commensurate delays finally we introduce the dual observability notion of approximate controllability and prove that the control system is exactly null controllable if and only if the transposed delay system tis continuously finally observable

i type of strong connectivity in l fuzzy topological spaces in this paper we mainly introduce and study r type of strong connectivity for a given l fuzzy topological space it preserves many good properties of connected sets in general topological spaces for example any union of r type of strongly connected sets with nonempty intersection is r type of strongly connected the images of irresolute order homomorphism of r type of strongly connected sets are r type of strongly connected

an algebraic characterization of closed small attainability subspaces of delay systems if small attainability subspaces of linear time delay systems are closed in a certain sobolev space the existence of lagrange multipliers for optimal control to small solutions is guaranteed this paper characterizes the required closedness property using an algebraic approach due to b jakubczyk as a main result it turns out that closedness is in an algebraic sense generic in the variety of system matrices a0 a1 b0 with rank a1 not greater than the dimension of the control space this is in contrast to known results on closedness of attainability subspaces playing an analogous role for optimal control to fixed final states instead of small solutions

horn approximations of empirical data abstract formal ai systems traditionally represent knowledge using logical formulas sometimes however a model based representation is more compact and enables faster reasoning than the corresponding formula based representation the central idea behind our work is to represent a large set of models by a subset of characteristic models more specifically we examine model based representations of horn theories and show that there are large horn theories that can be exactly represented by an exponentially smaller set of characteristic models we show that deduction based on a set of characteristic models requires only polynomial time as it does using horn theories more surprisingly abduction can be performed in polynomial time using a set of characteristic models whereas abduction using horn theories is np complete finally we discuss algorithms for generating efficient representations of the horn theory that best approximates a general set of models

optimal control of linear retarded systems to small solutions this paper deals with necessary optimality conditions for control of general linear retarded systems to small solutions here the final states at time t are required to generate small solutions of the uncontrolled system vanishing after t h where 0 is fixed this generalizes the fixed final state problem where 0 and for h includes problems with fixed reduced final state fx t where f is the structural operator of the delay system necessary optimality conditions in the form of a maximum principle are valid if a certain space called the small attainability sub space is closed in a sobolev space a sufficient criterion for this closedness property is indicated finally an example is discussed where the maximum principle for the fixed final state problem is not valid while the new problem with h can be solved by an application of the obtained results

fuzzy less strongly semiopen sets and fuzzy less strong semicontinuity abstract in this paper we first introduce the concepts of a fuzzy less strongly semiopen set a fuzzy less strongly semiclosed set fuzzy less strong semi interior and fuzzy less strong semiclosure we study their properties and discuss the relationships between these concepts and relevant concepts in fuzzy topological space finally we introduce the fuzzy less strongly continuous fuzzy less strongly semiopen and fuzzy less strongly semiclosed mappings on fuzzy topological space and establish their various characteristic properties

fuzzy strongly semiopen sets and fuzzy strong semicontinuity abstract in this paper we first introduce and study the fuzzy strongly semiopen and fuzzy strongly semiclosed sets in fuzzy space then we introduce the strong semi interior and strong semiclosure of a fuzzy set and kuratowski s 14 sets theorem of general topology is generalized finally we introduce the fuzzy strongly semicontinuous fuzzy strongly semiopen and fuzzy strongly semiclosed mappings on fuzzy topological spaces and also establish some of their characteristic properties and discuss relations between fuzzy continuous fuzzy semicontinuous and fuzzy strongly semicontinuous mappings

on the structure of armstrong relations for functional dependencies an armstrong relation for a set of functional dependencies fds is a relation that satisfies each fd implied by the set but no fd that is not implied by it the structure and size number of tuples of armstrong relatsons are investigated upper and lower bounds on the size of minimal sized armstrong relations are derived and upper and lower bounds on the number of distinct entries that must appear m an armstrong relation are given it is shown that the time complexity of finding an armstrong relation gwen a set of functional dependencies is precisely exponential in the number of attributes also shown s the falsity of a natural conjecture which says that almost all relations obeying a given set of fds are armstrong relations for that set of fds finally armstrong relations are used to generahze a result obtained by demetrovics using quite complicated methods about the possible sets of keys for a relauon

on criteria for closedness of an attainable set of a discrete neutral control system abstract this paper deals with the closedness of the attainable set in the function space w 1 2 l 2 of a linear neutral system with commensurate delays in state and control necessary and sufficient algebraic criteria expressed in terms of the system matrices for the closedness are derived by the additional restriction that the control is a scalar control another criterion for closedness based on the transfer matrix is indicated and used to verify the results

support set selection for abductive and default reasoning abstract of all the possible ways of computing abductive explanations the atms procedure is one of the most popular while this procedure is known to run in exponential time in the worst case the proof actually depends on the existence of queries with an exponential number of answers but how much of the difficulty stems from having to return these large sets of explanations here we explore abduction tasks similar to that of the atms but which return relatively small answers the main result is that although it is possible to generate some nontrivial explanations quickly deciding if there is an explanation containing a given hypothesis is np complete as is the task of generating even one explanation expressed in terms of a given set of assumption letters thus the method of simply listing all explanations as employed by the atms probably cannot be improved upon an interesting result of our analysis is the discovery of a subtask we call the support set selection task that is not only at the core of generating explanations but is also at the core of generating extensions in reiter s default logic moreover it is this subtask that accounts for the computational difficulty of both forms of reasoning this establishes for the first time a strong connection between computing abductive explanations and computing extensions in default logic