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15
Modal Logics for Qualitative Spatial Reasoning
, 1996
"... Spatial reasoning is essential for many AI applications. In most existing systems the representation is primarily numerical, so the information that can be handled is limited to precise quantitative data. However, for many purposes the ability to manipulate highlevel qualitative spatial information ..."
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Cited by 82 (12 self)
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Spatial reasoning is essential for many AI applications. In most existing systems the representation is primarily numerical, so the information that can be handled is limited to precise quantitative data. However, for many purposes the ability to manipulate highlevel qualitative spatial information in a flexible way would be extremely useful. Such capabilities can be proveded by logical calculi; and indeed 1storder theories of certain spatial relations have been given [20]. But computing inferences in 1storder logic is generally intractable unless special (domain dependent) methods are known. 0order modal logics provide an alternative representation which is more expressive than classical 0order logic and yet often more amenable to automated deduction than 1storder formalisms. These calculi are usually interpreted as propositional logics: nonlogical constants are taken as denoting propositions. However, they can also be given a nominal interpretation in which the constants stand...
Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of NonClassical Logics I
 Studia Logica
, 1998
"... The main goal of this paper is to explain the link between the algebraic and the Kripkestyle models for certain classes of propositional logics. We start by presenting a Priestleytype duality for distributive lattices endowed with a general class of wellbehaved operators. We then show that fin ..."
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Cited by 12 (6 self)
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The main goal of this paper is to explain the link between the algebraic and the Kripkestyle models for certain classes of propositional logics. We start by presenting a Priestleytype duality for distributive lattices endowed with a general class of wellbehaved operators. We then show that finitelygenerated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and nontopological Kripkestyle models for logics that are sound and complete with respect to varieties of distributive lattices with operators in the abovementioned classes. Introduction In the study of nonclassical propositional logics (and especially of modal logics) there are two main ways of defining interpretations or models. One possibility is to use algebras  usually lattices with operators  as models. Propositional variables are interpreted over elements of these algebraic models, an...
On Fibring Semantics for BDI Logics
 Logics in computer science
, 2002
"... This study examines BDI logics in the context of Gabbay's fibring semantics. We show that dovetailing (a special form of fibring) can be adopted as a semantic methodology to combine BDI logics. We develop a set of interaction axioms that can capture static as well as dynamic aspects of the ment ..."
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Cited by 9 (4 self)
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This study examines BDI logics in the context of Gabbay's fibring semantics. We show that dovetailing (a special form of fibring) can be adopted as a semantic methodology to combine BDI logics. We develop a set of interaction axioms that can capture static as well as dynamic aspects of the mental states in BDI systems, using Catach's incestual schema $G^{a, b, c, d}$. Further we exemplify the constraints required on fibring function to capture the semantics of interactions among modalities. The advantages of having a fibred approach is discussed in the final section.
Modal logics for topological spaces
 Thesis (Ph.D.)–City University of New York
, 1993
"... In this thesis we shall present two logical systems, MP and MP ∗ , for the purpose of reasoning about knowledge and effort. These logical systems will be ..."
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Cited by 6 (2 self)
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In this thesis we shall present two logical systems, MP and MP ∗ , for the purpose of reasoning about knowledge and effort. These logical systems will be
On canonical modal logics that are not elementarily determined. Logique et Analyse
 181:77— 101, 2003. Published October 2004. 20 Robert Goldblatt, Ian Hodkinson, and Yde
, 2004
"... There exist modal logics that are validated by their canonical frames but are not sound and complete for any elementary class of frames. Continuum many such bimodal logics are exhibited, including one of each degree of unsolvability, and all with the finite model property. Monomodal examples are als ..."
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Cited by 6 (5 self)
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There exist modal logics that are validated by their canonical frames but are not sound and complete for any elementary class of frames. Continuum many such bimodal logics are exhibited, including one of each degree of unsolvability, and all with the finite model property. Monomodal examples are also constructed that extend K4 and are related to the proof of noncanonicity of the McKinsey axiom. 1
Priestley Duality for SHnAlgebras and Applications to the Study of KripkeStyle Models for SHnLogics
 MultipleValued Logic { An International Journal
, 1999
"... The main goal of this paper is to show that the Priestley duality for SHnalgebras can help to establish a link between the algebraic and Kripkestyle semantics for SHn logics. We present a Priestley duality theorem for SHnalgebras, and note that the dual space of an SHnalgebra satis es in partic ..."
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Cited by 3 (2 self)
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The main goal of this paper is to show that the Priestley duality for SHnalgebras can help to establish a link between the algebraic and Kripkestyle semantics for SHn logics. We present a Priestley duality theorem for SHnalgebras, and note that the dual space of an SHnalgebra satis es in particular the properties of a Kripke model for SHnlogics. We then show that Priestley duality can help in proving the soundness and completeness of SHnlogics with respect to the class of SHnframes in a direct way, by using only soundness and completeness of SHnlogics with respect to the variety of SHnalgebras.
Algebraic Polymodal Logic: A Survey
 LOGIC JOURNAL OF THE IGPL
, 2000
"... This is a review of those aspects of the theory of varieties of Boolean algebras with operators (BAO's) that emphasise connections with modal logic and structural properties that are related to natural properties of logical systems. It begins with ..."
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Cited by 2 (0 self)
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This is a review of those aspects of the theory of varieties of Boolean algebras with operators (BAO's) that emphasise connections with modal logic and structural properties that are related to natural properties of logical systems. It begins with
Functional Monadic Bounded Algebras
, 2010
"... The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ∃ reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomor ..."
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Cited by 1 (1 self)
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The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ∃ reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions. We show that FMBA is characterised by the disjunction of the equations ∃E = 1 and ∃E = 0. We also define a weaker notion of “relatively functional ” algebra, and show that every member of MBA is isomorphic to a relatively functional one. In [1], an equationally defined class MBA of monadic bounded algebras was introduced. Each of these algebras comprises a Boolean algebra B with a distinguished element E, thought of as an existence predicate, and an operator ∃ on B reflecting the properties of the existential quantifier in logic without existence assumptions. MBA was shown to be generated by a certain proper
Fine’s Theorem on FirstOrder Complete Modal Logics
, 2011
"... Fine’s Canonicity Theorem states that if a modal logic is determined by a firstorder definable class of Kripke frames, then it is valid in its canonical frames. This article reviews the background and context of this result, and the history of its influence on further research. It then develops a n ..."
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Fine’s Canonicity Theorem states that if a modal logic is determined by a firstorder definable class of Kripke frames, then it is valid in its canonical frames. This article reviews the background and context of this result, and the history of its influence on further research. It then develops a new characterisation of when a logic is canonically valid, providing a precise point of distinction with the property of firstorder completeness. 1 The Canonicity Theorem and Its Impact In his PhD research, completed in 1969, and over the next halfdozen years, Kit Fine made a series of fundamental contributions to the semantic analysis and metatheory of propositional modal logic, proving general theorems about notable classes of logics and providing examples of failure of some significant properties. This work included the following (in order of publication): • A study [6] of logics that have propositional quantifiers and are defined