Showing papers on "Paraconsistent logic published in 1994"

What is a logical system

Abstract: 1. What is logic 2. Logic without model theory 3. Diagrams and the concept of logical system 4. General dynamics 5. What is a deductive system 6. The transmission of truth and the transmitting of abduction 7. What is a logical system? 8. What is a logical system? 9. Structure, consequence relation 10. Schematic consequence 11. Logical constants and punctuation marks 12. Finitary inductively presented logics 13. A-theory and its metatheory in FSo 14. General logics and logical frameworks 15. General algebraic logic, a perspective on What is Logic?

Concept Formation and Knowledge Revision

Abstract: Foreword. 1. Introduction. 2. The Psychology of Concepts and Concept Formation. 3. Concept Representation in a Paraconsistent Logic with Higher-Order Elements. 4. Knowledge Revision as a Concept Formation Context. 5. Demand-Driven Concept Formation. 6. Embeddedness. 7. Conclusion. A. MOBAL Software Info Page. B. Glossary of Symbols. References. Index.

Vivid Logic: Knowledge-Based Reasoning with Two Kinds of Negation

Abstract: General introduction.- Vivid knowledge representation and reasoning.- Partiality, paraconsistency and constructivity.- Vivid reasoning on the basis of facts.- Lindenbaum-algebraic semantics of logic programs.- Logic programming with strong negation and inexact predicates.- Vivid reasoning on the basis of rules.- Further topics, open problems.

Logical bilattices and inconsistent data

Abstract: The notion of a bilattice was first proposed by Ginsberg (1988) as a general framework for many applications. This notion was further investigated and applied for various goals by Fitting (1989, 1990, 1991, 1993). In this paper, we develop proof systems which correspond to bilattices in an essential way. We then show how to use those bilattices for efficient inferences from possibly inconsistent data. For this, we incorporate certain ideas of Kifer and Lozinskii (1992) concerning inconsistencies, which happen to well suit the framework of bilattices. The outcome is a paraconsistent logic with many desirable properties. >

Logic and Information Flow

Abstract: Logic and information flow, Jan van Eijck and Albert Visser a note on dynamic arrow logic, Johan van Benthem axiomatizing dynamic predicate logic with quantified dynamic logic, Jan van Eijck how logic emerges from the dynamics of information, Peter Gardenfors on action algebras, Dexter Kozen logic and control - how they determine the behaviour of presuppositions, Marcus Kracht classification domains and information links - a brief survey, Lawrence Moss and Jerry Seligman process algebra and dynamic logic, Alban Ponse a roadmap of some two-dimensional logics, Vaughan Pratt some new landmarks on the roadmap of two-dimensional logics, Hajnal Andreka et al meeting some neighbours, Maarten de Rijke actions under presuppositions, Albert Visser.

From Abstract Data Types to Logical Frameworks

Abstract: This paper surveys ways in which the ideas and concepts developed in the research field of abstract data types have undergone a vigorous process of generalization that has led to the development of axiomatic notions of logic and of expressive multiparadigm logics. On the one hand, the generalization from equational specifications to specifications in any logic requires general metalogical concepts making precise what logics are. Beginning with the notion of institution, several notions have been proposed to cover different needs arising in this task; we discuss these notions and summarize in particular the main ideas of the theory of general logics, which is a specific line of work in this area. On the other hand, the extension of equational logic in several directions to make specifications and programs more expressive has given rise to powerful multiparadigm logics in which other specification and programming paradigms can be cleanly combined with the equational one; we discuss several of these extensions, including rewriting logic, which unifies equational, Horn, object-oriented, and concurrent specification and programming.

Logic without model theory

Abstract: Arguably, model theory serves two main functions: (1) to explain the relationship between language and experience, and (2) to specify the notion of logical consequence. In this paper I shall propose the notion of`knowledge assimilation', the assimilation of new information into a knowledge base, as an alternative understanding of the way in which a knowledge base formulated in logic relates to externally generated input sentences that describe experience. I shall argue that the notion of logical consequence can also be understood within a knowledge assimilation framework, in terms of sentences that must hold no matter what stream of input sentences might arise in the future. Classical model theory can be understood as dealing with static relationships among individuals. It leads naturally therefore to possible world semantics and modal logic, in which models are understood as related to one another by accessibility relations. I shall argue in favour of a non-model-theoretic alternative to possible world semantics , an alternative which employs a syntactically rich vocabulary of terms representing time, events, situations and theories. Similarly to the way in which possible worlds can be viewed as arising from classical models, situations which cut across time and space in situation semantics can be viewed as arising from possible worlds. I shall argue for representing situations syntactically as theories and amalgamating object language and metalanguage as an alternative to situation semantics.

Naive Set Theory with Extensionality in Partial Logic and in Paradoxical Logic

Abstract: Two distinct and apparently “dual” traditions of non-classical logic, three-valued logic and paraconsistent logic, are considered here and a unified presentation of “easy-to-handle” versions of these logics is given, in which full naive set theory, i.e. Frege’s comprehension principle + extensionality, is not absurd. © 1994, Duke University Press. All Rights Reserved.

Sweet Reason: A Field Guide to Modern Logic

Abstract: Preface for the General Reader.- Preface for Logic Teachers: How to Use this Book in Logic Courses.- Introduction.- A Taste of Logic.- Everything All at Once and a Warning.- Statement Logic, Formal Languages, and Informal Arguments.- Valid Arguments, Convincing Arguments, and Punk Logic.- Predicates, Programs, and Antique Logic.- Deduction, Infinity, and a Haircut.- Symbolic Sophistication, Induction, and Business Logic.- Completeness, Disbelief, Debates, and Dinner.- Paradox, Impossibility, and the Law.- Notes.- References.- Hints.- Some Answers.- Index.

Fuzzy Logic or Lukasiewicz Logic: A Clarification

Abstract: 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.

A Note on Tableaux of Logic of Paradox

Abstract: The logic of paradox LP proposed by Priest [1979] is one of paraconsistent logics. One of the motivations behind paraconsistent logic, namely LP, is that it should not be the case that everything follows from a single contradiction. It must pay a price, however, that some classical inferences would be invalid in LP. In Priest's recent invention, the logic of minimal paradox LPm can overcome the drawback, such that paraconsistent logic would be equivalent to classical logic when there is not direct effect of a contradiction. Although some proof theories for LP were introduced, there has not yet been a satisfactory proof theory for LPm. We will propose a sound and complete tableaux for LPm in this article.

Paraconsistency and Beyond: A New Approach to Inconsistency Handling

Abstract: The expressive power of positive logic programs is enhanced by explicit negation by providing a natural and unambiguous way to assert negated information But by this, we are faced with the problem of dealing with contradictions in the database The ECSQ (for ‘ex contradictione sequitir quodlibet’) approach of classical logic, by which everything follows from a contradiction, thus resulting in the collapsing (or trivialization) of the system is certainly not a pragmatic approach towards handling inconsistency We propose an inconsistency handling concept — explicit paraconsistency, formalized as ApproachC, which is close in spirit to ‘paraconsistent’ approaches known from the logicophilosophical literature on non-classical logics handling inconsistency Furthermore, our approach goes beyond the paraconsistent horizon ie allowing nontrivial reasoning in presence of inconsistency We allow reasoning from inconsistent information, keep track of conclusions inferred from inconsistent premises and propagate a new horizon of reasoning involving elements ‘affected’ by inconsistency This we call reasoning beyond paraconsistency and formalize as Approach Cd

A knowledge representation perspective: logics for paraconsistent reasoning

Abstract: Paraconsistent logics are examined as an approach to knowledge representation devoted to the formalization of reasoning in the presence of contradictions. the adequacy of paraconsistent logics in such a perspective is described both on a general level and on a more specific level: discussion involves representative examples as well as special features (in the form of logical principles) of some significant paraconsistent logics. There is also a comparison of the paraconsistent logics approach with two alternative approaches, namely belief revision and non-monotonic logics. © 1994 John Wiley & Sons, Inc.

An axiomatic approach to the logical omniscience problem

Abstract: Standard models of knowledge have the unrealistic property that agents are logically omniscient in the sense that they know all logical implications of their information. While many nonstandard logics have been proposed to avoid this problem, none has an obvious claim as the "right" logic to use. I show how to derive such a logic as part of a representation of an agent's preferences. In this sense, the agent's logic is given the same basis as a utility function or subjective probability. I provide necessary and sufficient conditions for a given logic to be part of a representation of preferences. Unfortunately, the conditions are not easily interprettable in general. To illustrate them further, I summarize some of my earlier results (Lipman [1993a]) on when the agent's logic is a version of the logic of inconsistency proposed by Rescher and Brandom [1979]. I also discuss the difficulties of representing an agent as using Levesque's logic of implicit belief (Levesque [1984]) or some form of resource-bounded computation.

An Epistemic Logic of Situations.

Abstract: In this paper we present a first order epistemic logic that incorporates the essentially finite character of what is actually known by any knower. Our logic and language allows us to represent familiarity with individuals including individual situations. It is also a logic of l imited awareness in the manner of [FH88]. It is adequate for the syntactic characterization of the shared-si tuat ion account of common knowledge [Bar89]. Finally, it is sound and complete with respect to the presented semantics.

On Non-Alethic Logic

Abstract: Non-alethic logic was introduced in da Costa [3]. In this kind of logic the principles of tertium non datur and of contradiction are not valid; furthermore, nonalethic logic constitutes a generalization of both paraconsistent and paracomplete logics. Nowadays, paraconsistent and paracomplete logics constitutes an important subject among non-classical logics, being studied in many countries, especially in Brazil, Australia, Italy and the U.S.A. In this note we present one propositional system of non-alethic logic N1 and its corresponding first-order predicate system N 1 = .

Logic Programs with Refutation Rules.

Abstract: First-order probabilistic models are recognized as efficient frameworks to represent several realworld problems: they combine the expressive power of first-order logic, which serves as a knowledge representation language, and the capability to model uncertainty with probabilities. Among existing models, it is usual to distinguish the domain-frequency approach from the possible-worlds approach. Bayesian logic programs (BLPs, which conveniently encode possible-worlds semantics) and stochastic logic programs (SLPs, often referred to as a domain-frequency approach) are promising probabilistic logic models in their categories. This paper is aimed at comparing the respective expressive power of these frameworks. We demonstrate relations between SLPs’ and BLPs’ semantics, and argue that SLPs can encode the same knowledge as a subclass of BLPs. We introduce extended SLPs which lift the latter result to any BLP. Converse properties are reviewed, and we show how BLPs can define the same semantics as complete, range-restricted, non-recursive SLPs. Algorithms that translate BLPs into SLPs (and vice versa) are provided, as well as worked examples of the intertranslations of SLPs and BLPs.

On the Relationship between Assumption-based Framework and Autoepistemic Logic

Abstract: Assumption-based (AB) framework [BTK93] is a generalisation of abduction. It augments a theory with a set of admissible assumptions that it can defend against any attacks. Autoepistemic logic is a nonmonotonic logic about an ideal agent who reasons about her beliefs and ignorance introspectively. On the surface, these two formalisms look very different. A closer examination reveals many similarities. Indeed, BTK93 has shown that stable extensions in the AB framework of an autoepistemic theory correspond to the Moore's AE extensions of the theory. In this paper, we shall continue to establish some more relationships between the two formalisms. We first reformulate BTK's AB framework for AE logic with a modal approach. We then provide an AB framework for a revised preferred extension that neither subsumes nor being subsumed by Przymusinski's 3-valued AE logic. We then show that the AB framework for a revised complete extension of any consistent AE theory strictly subsumes Przymusinski's 3-valued AE logic. By exploiting the clear structure of the modally reformulated AB framework, we further define an AB framework for a reflexive preferred (cf. stable, complete) extension that integrates Schwarz 's reflexive AE logic with Przymusinski's 3-valued AE logic.