Topic
Modal operator
About: Modal operator is a research topic. Over the lifetime, 1151 publications have been published within this topic receiving 22865 citations. The topic is also known as: modal connective.
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01 Jan 2009
TL;DR: In this paper, a Prolog implementation of a decision procedure for a cut-free sequent calculus for logics with adjoint pairs of modal operators is given, which requires modification of some of the inference rules of the calculus.
Abstract: Sadrzadeh and Dyckhoff describe in [1] a cut-free sequent calculus for logics with adjoint pairs of modal operators. We give here a Prolog implementation of a decision procedure for this calculus and describe the simple mechanism for loop checking used to guarantee termination, which requires slight modification of some of the inference rules of the calculus.
3 citations
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TL;DR: In this paper, the authors consider propositional modal logic with two modal operators, and show that some important topological properties are expressible in this language, and present a few logics and proofs of f.m.p. and completeness theorems.
Abstract: We consider propositional modal logic with two modal operators $\Box$ and $\D$. In topological semantics $\Box$ is interpreted as an interior operator and $\D$ as difference. We show that some important topological properties are expressible in this language. In addition, we present a few logics and proofs of f.m.p. and of completeness theorems.
3 citations
TL;DR: The theorem analogous to Harrop’s theorem for these logics is proved and extended disjunction and existence properties are formulated.
Abstract: Extended disjunction and existence properties for predicate modal logics K, K4, T, S4 as well as these logics with the Barcan axiom, and the logic of provability are formulated. The theorem analogous to Harrop’s theorem for these logics is proved.
3 citations
TL;DR: This paper develops a general framework that subsumes three important classes of modal residuated lattices: interior algebras, Abelian ℓ-groups with conuclei, and negative cones of ™- groups with nuclei and shows that a categorical equivalence exists in each of these cases.
Abstract: Much work has been done on specific instances of residuated lattices with modal operators (either nuclei or conuclei). In this paper, we develop a general framework that subsumes three important classes of modal residuated lattices: interior algebras, Abelian l-groups with conuclei, and negative cones of l-groups with nuclei. We then use this framework to obtain results about these three cases simultaneously. In particular, we show that a categorical equivalence exists in each of these cases. The approach used here emphasizes the role played by reducts in the proofs of these categorical equivalences. Lastly, we develop a connection between translations of logics and images of modal operators.
3 citations
TL;DR: This paper reconstructs Quine's arguments against quantified modal logic, from the early 1940s to the early 1960s, and vindicates a qualified version of Quineʼs conjecture that quantifiedmodal logic is committed to essentialism.
3 citations