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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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Book ChapterDOI
Bartek Klin1
03 Sep 2005
TL;DR: The least (fibre-wise) of such liftings, L(B), is characterized for essentially any B, which has all the useful properties of the relation lifting due to Jacobs, without the usual assumption of weak pullback preservation.
Abstract: Every endofunctor B on the category Set can be lifted to a fibred functor on the category (fibred over Set) of equivalence relations and relation-preserving functions. In this paper, the least (fibre-wise) of such liftings, L(B), is characterized for essentially any B. The lifting has all the useful properties of the relation lifting due to Jacobs, without the usual assumption of weak pullback preservation; if B preserves weak pullbacks, the two liftings coincide. Equivalence relations can be viewed as Boolean algebras of subsets (predicates, tests). This correspondence relates L(B) to the least test suite lifting T(B), which is defined in the spirit of predicate lifting as used in coalgebraic modal logic. Properties of T(B) translate to a general expressivity result for a modal logic for B-coalgebras. In the resulting logic, modal operators of any arity can appear.

23 citations

Journal ArticleDOI
01 May 1969-Noûs
TL;DR: In this paper, the basic concepts of modal logic are presented from a philosophical perspective, both philosophical and formal, and the aim of this paper is to present a certain philosophical perspective.
Abstract: The aim of this paper is to present a certain philosophical perspective on the basic concepts of modal logic. The essentials of our approach, both philosophical and formal, are found in a previous paper,2 but will be recounted briefly in sections 1 and 3. Section 2 contains an intuitive explanation of our interpretation of the modal operators, and section 4 its formal counterpart. Section 5 considers quantification and singular terms in modal contexts. In section 6 we return to philosophical issues with the question whether t-he interpretation of modal language involves metaphysical commitments.

23 citations

Book ChapterDOI
01 Jan 1989
TL;DR: The question of the possibility of modal logic has apparently been disposed of for good, and the development of what has generally been taken to be a viable semantics (model theory) for modal Logic provides a basis from which Quine’s objections can apparently be answered satisfactorily and which yields a solid foundation for the different axiom systems formodal logic.
Abstract: The title of my paper may appear paradoxical, misplaced, or even worse, out of date. The possibility of a reasonable modal logic was denied by Quine on philosophical grounds, but his objections have been dead for a while, even though they have not yet been completely buried.1 What has made a crucial difference is the development of what has generally been taken to be a viable semantics (model theory) for modal logic.2 This semantics has provided a basis from which Quine’s objections can apparently be answered satisfactorily and which yields a solid foundation for the different axiom systems for modal logic. Thus the question of the possibility of modal logic has apparently been disposed of for good, and my title question accordingly may seem pointless.

23 citations

Proceedings Article
22 Jul 2007
TL;DR: In this paper, the propositional case of Reiter's and Scherl & Levesque's solutions to the frame problem can be modelled in dynamic epistemic logic (DEL), and an optimal regression algorithm for the latter is provided.
Abstract: We show how in the propositional case both Reiter's and Scherl & Levesque's solutions to the frame problem can be modelled in dynamic epistemic logic (DEL), and provide an optimal regression algorithm for the latter. Our method is as follows: we extend Reiter's framework by integrating observation actions and modal operators of knowledge, and encode the resulting formalism in DEL with announcement and assignment operators. By extending Lutz' recent satisfiability-preserving reduction to our logic, we establish optimal decision procedures for both Reiter's and Scherl & Levesque's approaches: satisfiability is NP-complete for one agent, PSPACE-complete for multiple agents and EXPTIME-complete when common knowledge is involved.

23 citations

Book ChapterDOI
TL;DR: This chapter deals with modal systems whose class of models is definable in first-order logic expanded with a least fixed point operator (FO(LFP), which implies that membership is decidable in polynomial time.
Abstract: Publisher Summary This chapter introduces the field of computational complexity in modal logic and provides some fundamental answers. The basic modal language, when interpreted over relational models, can be regarded as a decidable fragment of classical logic. The chapter explores the computational complexity of determining validity, or of performing tasks like model checking. The parameters that affect modal complexity results are discussed. The chapter deals with modal systems whose class of models is definable in first-order logic expanded with a least fixed point operator (FO(LFP)), which implies that membership is decidable in polynomial time. The actual algorithms for deciding the satisfiability problem under constraints and the local satisfiability problem for a number of typical cases are reviewed. Hintikka set elimination is an algorithm, which constructs the model whose idea comes straight from the proof of the truth lemma. A globally satisfiable constraint, which, when satisfied, forces a branch in the model containing an exponential number of different Hintikka set is created.

23 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202222
202138
202035
201946
201844