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991,035
Labelled Tableaux for NonNormal Modal Logics
 In Sixth Conference of the Italian Association for Arti Intelligence, AI*IA '99
, 2000
"... In this paper we show how to extend \KEM, a tableaulike proof system for normal modal logic, in order to deal with classes of nonnormal modal logics, such as monotonic and regular, in a uniform and modular way. ..."
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Cited by 12 (7 self)
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In this paper we show how to extend \KEM, a tableaulike proof system for normal modal logic, in order to deal with classes of nonnormal modal logics, such as monotonic and regular, in a uniform and modular way.
From Classical to Normal Modal Logics
 Proof Theory of Modal Logic
, 1996
"... . Classical modal logics generally neither possess the necessitation rule nor the Kaxiom. Their semantics being in terms of minimal models, several specialisations of these have been given such as augmented minimal models, models with queer worlds or models with inaccessible worlds. In this pa ..."
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Cited by 13 (1 self)
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. In this paper we exhibit exact translations from these families into normal multimodal logics. Such translations allow to reuse the proof systems that have been developed for the latter. 1 Introduction Classical modal logics (Segerberg 1971, Chellas 1980) are weaker than the wellknown normal modal logics
Binary Logics, Orthologics and their Relations to Normal Modal Logics
 Advances in Modal Logic
"... this paper. The modal language ML consists of:(1) a set of propositional variables fq 1 ; q 2 ; : : :g, (2) a propositional constant ?, (3) conjunction ^, (4) negation :, (5) necessity 2, and (6) a pair of parentheses (; ). The set of formulas of this language is denoted by . The smallest normal mo ..."
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Cited by 1 (0 self)
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modal logic is denoted by K. For a set of formulas the smallest normal modal logic that contains is denoted by K. For a modal logic M, the class of all normal modal logics above M is denoted by Next(M)
Calculi for intuitionistic normal modal logic
 In Proceedings of Programming and Programming Languages
, 2007
"... This paper provides a callbyname and a callbyvalue term calculus, both of which have a CurryHoward correspondence to the box fragment of the intuitionistic modal logic IK. The strong normalizability and the confluency of the calculi are shown. Moreover, we define a CPS transformation from the c ..."
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Cited by 2 (1 self)
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This paper provides a callbyname and a callbyvalue term calculus, both of which have a CurryHoward correspondence to the box fragment of the intuitionistic modal logic IK. The strong normalizability and the confluency of the calculi are shown. Moreover, we define a CPS transformation from
Proving unprovability in some normal modal logics
 Bulletin of the Section of Logic. Polish Academy of Science
, 1991
"... The present communication suggests deductive systems for the operator ⊣ of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of ̷Lukasiewicz: for every formula φ either ⊢ φ or ⊣ φ (but not both) is deriva ..."
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Cited by 3 (0 self)
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The present communication suggests deductive systems for the operator ⊣ of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of ̷Lukasiewicz: for every formula φ either ⊢ φ or ⊣ φ (but not both
Strongly Analytic Tableaux for Normal Modal Logics
, 1994
"... A strong analytic tableau calculus is presentend for the most common normal modal logics. The method combines the advantages of both sequentlike tableaux and prefixed tableaux. Proper rules are used, instead of complex closure operations for the accessibility relation, while non determinism and cu ..."
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Cited by 50 (14 self)
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A strong analytic tableau calculus is presentend for the most common normal modal logics. The method combines the advantages of both sequentlike tableaux and prefixed tableaux. Proper rules are used, instead of complex closure operations for the accessibility relation, while non determinism
Nearly every normal modal logic is paranormal
"... The principal interest is philosophical: not to confine oneself to what is necessary for (current) practice, but to see what is possible by way of theoretical analysis. —Kreisel (1970). An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences ..."
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negation, nearly every normal modal logic, in its ordinary language and in
15 Binary Logics, Orthologics and their Relations to Normal Modal Logics Yutaka Miyazaki
"... abstract. We study the relation between the class Ext(O) of orthologics and the class Next(KTB) of normal modal logics over KTB by means of embeddings of logics. First we introduce binary logics, which are generalizations of orthologics, as logics that are embeddable into some normal modal logics. W ..."
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abstract. We study the relation between the class Ext(O) of orthologics and the class Next(KTB) of normal modal logics over KTB by means of embeddings of logics. First we introduce binary logics, which are generalizations of orthologics, as logics that are embeddable into some normal modal logics
Relations Between Propositional Normal Modal Logics: An Overview
 Journal of Logic and Computation
, 1995
"... The modal logic literature is notorious for multiple axiomatisations of the same logic and for conflicting overloading of axiom names. Many of the interesting interderivability results are still scattered over the often hard to obtain classics. We catalogue the most interesting axioms, their numerou ..."
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Cited by 6 (3 self)
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The modal logic literature is notorious for multiple axiomatisations of the same logic and for conflicting overloading of axiom names. Many of the interesting interderivability results are still scattered over the often hard to obtain classics. We catalogue the most interesting axioms
Lukasiewicz’s 4valued Logic and Normal Modal Logics
"... Abstract. In this paper, we investigate the Lukasiewicz’s 4valued modal logic based on the Aristotele’s modal syllogistic. We present a new interpretation of the set of algebraic truth values by introducing the truth and knowledge orderings similar to those in Belnap’s 4valued bilattice but by re ..."
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but by replacing the original Belnap’s negation with the lattice pseudocomplement instead. Based on it, we develop a formal modal Boolean algebra for Lukasiewicz’s system. We show that this modal algebra corresponds to the standard normal modal logic and develop an autoreferential Kripkestyle semantics for it
Results 1  10
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