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ManyValued Modal Logics
 Fundamenta Informaticae
, 1992
"... . Two families of manyvalued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite manyvalued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds a ..."
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Cited by 215 (16 self)
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. Two families of manyvalued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite manyvalued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be manyvalued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established. 1 Introduction The logics that have appeared in artificial intelligence form a rich and varied collection. While classical (and maybe intuitionistic) logic su#ces for the formal development of mathematics, artificial intelligence has found uses for modal, temporal, relevant, and manyvalued logics, among others. Indeed, I take it as a basic principle that an application should find (or create) an appropriate logic, if it needs one, rather than reshape the application to fit some narrow class of `established' logics. In this paper I want to enlarge the variety of logics...
Fixpoint semantics for logic programming  a survey
, 2000
"... The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close para ..."
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Cited by 105 (0 self)
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The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies.
Kleene’s threevalued logics and their children
 Fundamenta Informaticae
, 1994
"... Abstract. Kleene’s strong threevalued logic extends naturally to a fourvalued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it fourvalued analogs of Kleene’s weak threevalued logic, and the asymmetri ..."
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Cited by 25 (4 self)
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Abstract. Kleene’s strong threevalued logic extends naturally to a fourvalued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it fourvalued analogs of Kleene’s weak threevalued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear bilattices the extensions do not produce any new equivalences. 1
WellFounded Semantics, Generalized
 In Proceedings of International Symposium on Logic Programming
, 1991
"... Classical fixpoint semantics for logic programs is based on the TP immediate consequence operator. The Kripke/Kleene, threevalued, semantics uses #P , which extends TP to Kleene's strong threevalued logic. Both these approaches generalize to cover logic programming systems based on a wide class of ..."
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Cited by 13 (2 self)
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Classical fixpoint semantics for logic programs is based on the TP immediate consequence operator. The Kripke/Kleene, threevalued, semantics uses #P , which extends TP to Kleene's strong threevalued logic. Both these approaches generalize to cover logic programming systems based on a wide class of logics, provided only that the underlying structure be that of a bilattice. This was presented in earlier papers. Recently wellfounded semantics has become influential for classical logic programs. We show how the wellfounded approach also extends naturally to the same family of bilatticebased programming languages that the earlier fixpoint approaches extended to. Doing so provides a natural semantics for logic programming systems that have already been proposed, as well as for a large number that are of only theoretical interest. And finally, doing so simplifies the proofs of basic results about the wellfounded semantics, by stripping away inessential details. 1 Introduction There hav...
A Theory of Truth that prefers falsehood
 Journal of Philosophical Logic
, 1994
"... We introduce a subclass of Kripke's fixed points in which falsehood is the preferred truth value. In all of these the truthteller evaluates to false, while the liar evaluates to undefined (or overdefined). The mathematical structure of this family of fixed points is investigated and is shown to h ..."
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We introduce a subclass of Kripke's fixed points in which falsehood is the preferred truth value. In all of these the truthteller evaluates to false, while the liar evaluates to undefined (or overdefined). The mathematical structure of this family of fixed points is investigated and is shown to have many nice features. It is noted that a similar class of fixed points, preferring truth, can also be studied. The notion of intrinsic is shown to relativize to these two subclasses. The mathematical ideas presented here originated in investigations of socalled stable models in the semantics of logic programming. 1 Introduction Briefly stated, the job of a theory of truth is to assign truth values to sentences in a language allowing selfreference, in a way that respects intuition while avoiding paradox. Of course this can not be done in the framework of classical, twovalued logic because of liar sentences. Some generalization allowing partial truth assignments, or perhaps contradic...
On Prudent Bravery and Other Abstractions
 In preparation
, 1994
"... ions Melvin Fitting fitting@alpha.lehman.cuny.edu Dept. Mathematics and Computer Science Lehman College (CUNY), Bronx, NY 10468 Depts. Computer Science, Philosophy, Mathematics Graduate Center (CUNY), 33 West 42nd Street, NYC, NY 10036 # October 13, 1994 Abstract A special class of partial ..."
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Cited by 2 (2 self)
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ions Melvin Fitting fitting@alpha.lehman.cuny.edu Dept. Mathematics and Computer Science Lehman College (CUNY), Bronx, NY 10468 Depts. Computer Science, Philosophy, Mathematics Graduate Center (CUNY), 33 West 42nd Street, NYC, NY 10036 # October 13, 1994 Abstract A special class of partial stable models, the intrinsic ones, is singled out for consideration, and attention is drawn to the largest one, which we designate as the prudently brave one. It is the largest partial stable model that is compatible with every partial stable model. As such, it is an object of natural interest. Its existence follows from general properties of monotonic functions, so it is a robust notion. The proofs given concerning intrinsic stable models are not new, but they appeared earlier in quite di#erent contexts. What we do, essentially, is call the attention of the logic programming and nonmonotonic reasoning community to them. We further show the entire development fits into the bilattice ...
A new conditional for naïve truth theory
"... Abstract: In this paper the a logic, TJK +, suitable for reasoning disquotationally about truth is presented and shown to have a standard model. This work improves on Hartry Field’s recent results establishing consistency and ωconsistency of truththeories with strong conditional logics. A novel me ..."
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Abstract: In this paper the a logic, TJK +, suitable for reasoning disquotationally about truth is presented and shown to have a standard model. This work improves on Hartry Field’s recent results establishing consistency and ωconsistency of truththeories with strong conditional logics. A novel method utilising the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have so far failed to provide. 1
Inferentialist De ationism
, 2010
"... According to the de ationist about truth, the English expression `... is true ' (the `truth predicate') does not stand for a property. To say that `Snow is white ' is true is just saying that snow is white. However, little agreement has been achieved so far how this `just ' is to be understood. ..."
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According to the de ationist about truth, the English expression `... is true ' (the `truth predicate') does not stand for a property. To say that `Snow is white ' is true is just saying that snow is white. However, little agreement has been achieved so far how this `just ' is to be understood.
Midwest Studies in Philosophy, XXXII (2008) Where the Paths Meet: Remarks on Truth and Paradox*
"... The study of truth is often seen as running on two separate paths: the nature path and the logic path.The former concerns metaphysical questions about the “nature, ” if any, of truth. The latter concerns itself largely with logic, particularly logical issues arising from the truththeoretic paradoxe ..."
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The study of truth is often seen as running on two separate paths: the nature path and the logic path.The former concerns metaphysical questions about the “nature, ” if any, of truth. The latter concerns itself largely with logic, particularly logical issues arising from the truththeoretic paradoxes. Where, if at all, do these two paths meet? It may seem, and it is all too often assumed, that they do not meet, or at best touch in only incidental ways. It is often assumed that work on the metaphysics of truth need not pay much attention to issues of paradox and logic; and it is likewise assumed that work on paradox is independent of the larger issues of metaphysics. Philosophical work on truth often includes a footnote anticipating some resolution of the paradox, but otherwise tends to take no note of it. Likewise, logical work on truth tends to have little to say about metaphysical presuppositions, and simply articulates formal theories, whose strength may be measured, and whose properties may be discussed. In practice, the paths go their own ways. Our aim in this paper is somewhat modest. We seek to illustrate one point of intersection between the paths. Even so, our aim is not completely modest, as the point of intersection is a notable one that often goes unnoticed. We argue that the “nature ” path impacts the logic path in a fairly direct way. What one can and must