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Showing papers on "Paraconsistent logic published in 1997"


Proceedings ArticleDOI
28 May 1997
TL;DR: The general result, challenging the existence of many-valued logic, according to which every logic may be seen as two-valued is discussed.
Abstract: Firstly we examine the definition of many-valued logic within the framework of (logical) matrix theory. Secondly we discuss the general result, challenging the existence of many-valued logic, according to which every logic may be seen as two-valued. Thirdly we analyze the principle of bivalence and show that it appears at a deeper level than one usually thinks.

204 citations


Journal ArticleDOI
01 Oct 1997-Mind
TL;DR: Jaskowski's paraconsistent discussive logic-a logic which admits truth value gluts-can be defended by reflecting on similarities between it and the popular supervaluationist analysis of vagueness already in the philosophical literature.
Abstract: One of the few points of agreement to be found in mainstream responses to the logical and semantic problems generated by vagueness is the view that if any modification of classical logic and semantics is required at all then it will only be such as to admit underdetermined reference and truth-value gaps. Logics of vagueness including many valued logics, fuzzy logics, and supervaluation logics all provide responses in accord with this view. The thought that an adequate response might require the recognition of cases of overdetermination and truth value gluts has few supporters. This imbalance lacks justification. As it happens, Jaskowski's paraconsistent discussive logic-a logic which admits truth value gluts-can be defended by reflecting on similarities between it and the popular supervaluationist analysis of vagueness already in the philosophical literature. A simple dualisation of supervaluation semantics results in a paraconsistent logic of vagueness based on what has been termed subvaluational semantics.

146 citations


Journal ArticleDOI
TL;DR: This paper generalizes this idea to the case where entire components — for example, the proof theory — of one of the logics involved may be completely missing, so that the appropriate mapping could not even be defined.

82 citations


Journal ArticleDOI
TL;DR: This paper shows that this ac- count gives a sound and complete semantics for Priest's paraconsistent logic LP, which uses materials any modal logician has at hand.
Abstract: Paraconsistent logics are often semantically motivated by consider- ing "impossible worlds." Lewis, in "Logic for equivocators," has shown how we can understand paraconsistent logics by attributing equivocation of mean- ings to inconsistent believers. In this paper I show that we can understand para- consistent logics without attributing such equivocation. Impossible worlds are simply sets of possible worlds, and inconsistent believers (inconsistently) be- lieve that things are like each of the worlds in the set. I show that this ac- count gives a sound and complete semantics for Priest's paraconsistent logic LP, which uses materials any modal logician has at hand.

60 citations


Journal ArticleDOI
TL;DR: The paper demonstrates the existence of paraconsistent logic models and provides a complete taxonomy of the finite ones, which model theories properly containing all the sentences of first order arithmetic.
Abstract: The paper concerns interpretations of the paraconsistent logic LP which model theories properly containing all the sentences of first order arithmetic. The paper demonstrates the existence of such models and provides a complete taxonomy of the finite ones.

45 citations


Journal ArticleDOI
TL;DR: The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of ‘worlds’ in order to study various philosophical and logical phenomena.
Abstract: In this paper, the author derives a metaphysical theory of impossible worlds from an axiomatic theory of abstract objects The underlying logic of the theory is classical Impossible worlds are not taken to be primitive entities but are instead characterized intrinsically using a definition that identifies them with, and reduces them to, abstract objects The definition is shown to be a good one–the proper theorems derivable from the definition assert that impossible worlds have the important characteristics that philosophers suppose them to have None of these consequences, however, imply that any contradiction is true (though contradictions can be "true at" impossible worlds) This classically-based conception of impossible worlds provides a subject matter for paraconsistent logic and demonstrates that there need be no conflict between the laws of paraconsistent logic and the laws of classical logic, for they govern different kinds of worlds It is argued that the resulting theory constitutes a theory of genuine (as opposed to ersatz) impossible worlds However, impossible worlds are not needed to distinguish necessarily equivalent propositions or for the treatment of the propositional attitudes, since the underlying theory of propositions already has that capacity

44 citations


Journal ArticleDOI
TL;DR: A survey of epistemic logics for the logical omniscience problem can be found in this article, where the authors present a collection of logics that can be used to model skeptical and credulous agents.
Abstract: This survey brings together a collection of epistemic logics and discusses their approaches in alleviating the logical omniscience problem. Of particular note is the logic of implicit and explicit belief. Explicit belief refers to information actively held by an agent, while implicit belief refers to the logical consequence of explicit belief. Ramifications of Levesque's logic include nonstandard epistemic logic and the logics of awareness and local reasoning. Models of nonstandard epistemic logic are defined with respect to nonstandard proportional logic to weaken its semantics. In the logic of awareness, an agent can only believe a concept that it is aware of. Closely related to awareness are S-1 and S-3 epistemic operators which can be used to model skeptical and credulous agents. The logic of local reasoning provides a semantics for representing the fact that agents can have different clusters of beliefs which may contradict each other. Other variations include epistemic structures which are generalizations of the logic of local reasoning and fusion epistemic models which provide an account that agents can combine information conjunctively or disjunctively. Another closely related approach is the logic of explicit propostions which captures the insight that agents can hold beliefs independently without putting them together.

41 citations


Book
01 Jan 1997

31 citations



Proceedings ArticleDOI
12 Nov 1997
TL;DR: An extension of the ParaLog logic programming language, called Para log e, that allows direct handling of inconsistency is described, which will widen the scope of logic programming applications in environments presenting conflicting beliefs and contradictory information.
Abstract: Inconsistency is a natural phenomenon arising from the description of the real world. This phenomenon may be encountered in several situations. Nevertheless, human beings are capable of reasoning adequately. The automation of such reasoning requires the development of formal theories. ParaLog (Paraconsistent Logic) was proposed by N.C.A. da Costa et al. (1995) to provide tools to reason about inconsistencies. This paper describes an extension of the ParaLog logic programming language, called ParaLog e, that allows direct handling of inconsistency. Languages such as ParaLog e, which are capable of merging classical logic programming concepts with those of inconsistency, widen the scope of logic programming applications in environments presenting conflicting beliefs and contradictory information.

16 citations


Journal Article
TL;DR: This paper presents a theory of probability based on the paraconsistent logic D4 and defines two sorts of Bayesian updating so that agents' beliefs become more consistent as well as more complete through updating.
Abstract: This paper presents a theory of probability based on the paraconsistent logic D4. The resulting probability functions are then used to define two sorts of Bayesian updating. One sort of updating merely uses the simple rule of conditionalisation. The other sort adds a wrinkle to the simple rule so that agents' beliefs become more consistent as well as more complete through updating.

Book ChapterDOI
28 Jul 1997
TL;DR: This work motivates the use of paraconsistency and the detection of contradiction supported conclusions by recourse to examples and shows how to implement two recent modal contradiction related constructs in the language of extended logic programs to gain explicit control of contradiction propagation.
Abstract: We begin by motivating the use of paraconsistency and the detection of contradiction supported conclusions by recourse to examples. Next we overview WFSXP and present its embedding into WFS. We then address the problem of detecting contradiction support and relate it to WFSXp's intrinsic properties. Afterwards, we show how to implement two recent modal contradiction related constructs in the language of extended logic programs in order to gain explicit control of contradiction propagation. We finish by making comparisons and drawing some conclusions.

Journal ArticleDOI
TL;DR: This article pointed out that MWSLs fail to understand the logic and properties of my theory almost every time it differs from their theory, and they have ignored explanations in my paper that would serve to correct their misrepresentations of my theories.
Abstract: T he comment by Markovsky, Willer, l Simpson, and Lovaglia (1997, henceforward MWSL) contains fundamental flaws in their discussion of the main properties of my theory and mathematical model and in their criticism of my method of comparing predictions from the model with the empirical results, which I presented in my original paper (Yamaguchi 1996). MWSL fail to understand the logic and properties of my theory almost every time it differs from their theory, and they have ignored explanations in my paper that would serve to correct their misrepresentations of my theory. This reply provides an opportunity for me to demonstrate that, in their comment, MWSL selectively ignore those parts of my theory that invalidate their assertions.

Proceedings Article
23 Sep 1997
TL;DR: The paper develops in the λ Sym PA system a formal proof for a formula that can be seen as a simple but meaningful program specification and shows how to restrict the system in order to get confluence without loosing its computational features.
Abstract: λ Sym PA is a natural deduction system for Peano Arithmetic that was developed in order to provide a basis for the programming with-proofs paradigm in a classical logic setting. In the paper we analyze one of its main features: non-confluence. After looking at which rules can cause non-confluence, we develop in the system a formal proof for a formula that can be seen as a simple but meaningful program specification. The computational behaviour of the corresponding term will be analysed by interpreting it as a (higher-order communicating) process formed by distinct subprocesses which co-operate in different ways, producing different results, according to the reduction strategy used. We also show how to restrict the system in order to get confluence without loosing its computational features. The restricted system enables us to argue for the expressive power of symmetric and non-deterministic calculi like λ Sym PA .

Proceedings ArticleDOI
30 Jun 1997
TL;DR: A logic of enactment with local reasoning is presented that is able to resson consistently in the presence of inconsistent enacted norms and expert Systerns can now reason with the use of normal first-order logic within a cluster instead of nonmonotonic logic approaches.
Abstract: In the article, we present a logic of enactment with local reasoning. The basic idea behind this treatment is that sets of aurhorities may enact conilicting normative rules, depending on the frame of reference. The main strength of the presented theory is that we are now able to resson consistently in the presence of inconsistent enacted norms. In most legal support/expert systems only the applicable norms are considered. It is impossible in these systems to talk about the rules that select applicable norms explicitly. This is the main disadvantage of using non-monotonic logic logics with minimal models and argumentation approaches. In these theories we can reason with inconsistent information, but the level is always of applicable norms. One cannot reason about enacted norms which are not applicable. Any derivation using these norms is blocked through the implicit consistency requirement of the non-monotonic modus panens rule. In the paper we give a theory to describe enacted norms and applicable norms separately. This can be seen as naming the minimal models with sets of nuthorifies. Making this explicit in a modal op erator enables us also to reason about enacted norms that are not applicable (within a non-preferred minimal logic). Therefore, we introduce the logic for enactment with local reasoning. In the logic for enactment we treat NA, as a modal operator, with Ai E NA and NA the set of normative authorities. The formula NAP : B is read as ‘the set Ai of normative authorities enacted the norm 8’. The system Ent for enactment with respect to set NA is a restricted version of the system weak 55 or I-D45 (Chellas 1980), in the sense that we are not dealing with nested enactment. On the other hand we add an extra rule to express the relation between sets of authorities: ,,t$ ..@. %In system Ent there is a property that is very unrealistic, which nevertheless holds: NA, : B -) ~NA, : 10: consistency of enactments. As we already mentioned in the introduction, it is a frequent phenomenon that authorities enacted conflicting norms. Frank Dignum Eindhoven University of Technology Dept. of Mathematics and Computer Science P.O.box 513, 5600 MB Eindhoven The Netherlands email: dignum@win.tue.nl In the logic of local reasoning (Fagin SC Halpern 1988), there is not necessarily one set of worlds that a set of authorities thinks possible, but rather a number of sets, each one corresponding to a different set of enacted norms. In a given situation, such a set of enacted norms by A; is a ma&ma1 consistent sei of the set EA, of explicitly enacted norms by Ai. The basic idea is that a set of authorities may enact inconsistent norms, but these conflicting norms are not applicable at the same time (depending on the situation). We view a cluster as representing the worlds the set of authorities thinks are possible in a given frame of reference, when he is focusing on a certain set of issues (Royakkers and Dignum 1997). We distinguish weak and strong enactment: Nz, : 8: the set Ai of authorities enacted 0 in a weak sense, i.e. within some cluster considered by A;; N& : 8: the set Ai of authorities enacted B in a strong sense, i.e. within all clusters considered by Ai. A set of authorities may now enact inconsistent norms: Nxi : 0 A Ni : 70 is satisfiable, since in one cluster the set Ai conkiders that 0 is applicable, while in another the set considers 10 applicable. N;, : 0 represents that the set Ai of authorities considers that 0 is applicable in any frame of reference. Thii means that 0 is not conflicting with any other norm enacted by the set Ai of authorities. However, the norm can be conflicting with a norm enacted by a superset Ai of Ai (Ai C Ai)The main advantage of this theory is that expert Systerns can now reason with the use of normal first-order logic within a cluster instead of using nonmonotonic

Book ChapterDOI
01 Jan 1997

Journal ArticleDOI
TL;DR: De Morgan’s explanation of the validity of arguments that involve relational notions is discussed, and the point that his endeavour is not successful in that the rules that made up his new logic are not sound are made.
Abstract: This paper is concerned with De Morgan’s explanation of the validity of arguments that involve relational notions. It discusses De Morgan’s expansion of traditional logic aimed at accommodating those inferences, and makes the point that his endeavour is not successful in that the rules that made up his new logic are not sound. Nevertheless, the most important scholarly work on De Morgan’s logic, and contrary to that De Morgan’s mistake is not beyond repair. The rules that determine his new logic are in fact monotonie replacement rules. And provided they are restricted in the correct way, these rules are demonstrably sound


Book ChapterDOI
01 Jan 1997
TL;DR: It is universally agreed that the use of signs is a most important aid and that without them no extended process or reasoning could be conducted.
Abstract: Reasoning is for the most part carried on by the aid of signs. It has been contended by some writers that it can only be conducted by this agency; others maintain that the use of signs is not indispensable and this is the more probable opinion. But it is universally agreed that the use of signs is a most important aid and that without them no extended process or reasoning could be conducted

Book ChapterDOI
01 Jan 1997
TL;DR: This paper attempts to survey recent issues in Logic, Language and Computation, and gives an exposition of recent topics in formal logic, formal semantics and artificial intelligence (AI).
Abstract: This paper attempts to survey recent issues in Logic, Language and Computation, and also serves as an introduction to the present book. Of course, my survey is not exhaustive, but it will provide background information to the reader for understanding current topics in these areas. In particular, I give an exposition of recent topics in formal logic, formal semantics and artificial intelligence (AI). I also try to discuss some important directions for future work in connection with several contributions in this book.