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  1. A Catalog ofWeak Many-Valued Modal Axioms and their Corresponding Frame Classes.Costas D. Koutras - 2003 - Journal of Applied Non-Classical Logics 13 (1):47-71.
    In this paper we provide frame definability results for weak versions of classical modal axioms that can be expressed in Fitting's many-valued modal languages. These languages were introduced by M. Fitting in the early '90s and are built on Heyting algebras which serve as the space of truth values. The possible-worlds frames interpreting these languages are directed graphs whose edges are labelled with an element of the underlying Heyting algebra, providing us a form of many-valued accessibility relation. Weak axioms of (...)
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  • Many-valued modal logics: A simple approach: Many-valued modal logics: A simple approach.Graham Priest - 2008 - Review of Symbolic Logic 1 (2):190-203.
    1.1 In standard modal logics, the worlds are 2-valued in the following sense: there are 2 values that a sentence may take at a world. Technically, however, there is no reason why this has to be the case. The worlds could be many-valued. This paper presents one simple approach to a major family of many-valued modal logics, together with an illustration of why this family is philosophically interesting.
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  • Hybrid Logic and its Proof-Theory.Torben Braüner - 2010 - Dordrecht and New York: Springer.
    This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model. This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems (...)
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  • Many-valued hybrid logic.Jens Ulrik Hansen, Thomas Bolander & Torben Braüner - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 111-132.
    In this paper we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be "intermediate" logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained (...)
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  • A Duality for the Algebras of a Łukasiewicz n + 1-valued Modal System.Bruno Teheux - 2007 - Studia Logica 87 (1):13-36.
    In this paper, we develop a duality for the varieties of a Łukasiewicz n + 1-valued modal System. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived and we propose some ideas for future research.
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  • On a Simple 3-valued Modal Language and a 3-valued Logic of ‘not-fully-justified’ Belief.Costas Koutras, Christos Nomikos & Pavlos Peppas - 2008 - Logic Journal of the IGPL 16 (6):591-604.
    In this paper, we advocate the usage of the family of Heyting-valued modal logics, introduced by M. Fitting, by presenting a simple 3-valued modal language and axiomatizing an interesting 3-valued logic of belief. We give two simple bisimulation relations for the modal language, one that respects non-falsity and one that respects the truth value. The doxastic logic axiomatized, apart from being interesting in its own right for KR applications, it comes with an underlying 3-valued propositional logic which is a syntactic (...)
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  • Frame constructions, truth invariance and validity preservation in many-valued modal logic.Pantelis E. Eleftheriou & Costas D. Koutras - 2005 - Journal of Applied Non-Classical Logics 15 (4):367-388.
    In this paper we define and examine frame constructions for the family of manyvalued modal logics introduced by M. Fitting in the '90s. Every language of this family is built on an underlying space of truth values, a Heyting algebra H. We generalize Fitting's original work by considering complete Heyting algebras as truth spaces and proceed to define a suitable notion of H-indexed families of generated subframes, disjoint unions and bounded morphisms. Then, we provide an algebraic generalization of the canonical (...)
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  • General approach to many valued Kripke models.Szymon Frankowski - 2006 - Bulletin of the Section of Logic 35 (1):11-26.
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  • (1 other version)Bisimulations and Boolean Vectors.Melvin Fitting - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 97-125.
    A modal accessibility relation is just a transition relation, and so can be represented by a {0, 1} valued transition matrix. Starting from this observation, I first show that the machinery of matrices, over Boolean algebras more general than the two-valued one, is appropriate for investigating multi-modal semantics. Then I show that bisimulations have a rather elegant theory, when expressed in terms of transformations on Boolean vector spaces. The resulting theory is a curious hybrid, fitting between conventional modal semantics and (...)
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  • Encoding modal logics in logical frameworks.Arnon Avron, Furio Honsell, Marino Miculan & Cristian Paravano - 1998 - Studia Logica 60 (1):161-208.
    We present and discuss various formalizations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hilbert- and Natural Deduction-style proof systems for representing both truth (local) and validity (global) consequence relations for various Modal Logics. We introduce several techniques for encoding the structural peculiarities of necessitation rules, in the typed -calculus metalanguage of the Logical Frameworks. These formalizations yield readily proof-editors for Modal Logics when implemented in Proof Development Environments, such as Coq or LEGO.
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  • How True It Is = Who Says It’s True.Melvin Fitting - 2009 - Studia Logica 91 (3):335-366.
    This is a largely expository paper in which the following simple idea is pursued. Take the truth value of a formula to be the set of agents that accept the formula as true. This means we work with an arbitrary Boolean algebra as the truth value space. When this is properly formalized, complete modal tableau systems exist, and there are natural versions of bisimulations that behave well from an algebraic point of view. There remain significant problems concerning the proper formalization, (...)
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  • Propositional dynamic logic for searching games with errors.Bruno Teheux - 2014 - Journal of Applied Logic 12 (4):377-394.
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  • Definable classes of many valued Kripke frames.Szymon Frankowski - 2006 - Bulletin of the Section of Logic 35 (1):27-36.
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