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  1. 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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  • 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 (finite) 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 (...)
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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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  • 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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