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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TL;DR: In this article, the authors prove fundamental properties of monotone modal operators on bounded commutative integral residuated lattices (CRL) and give a positive answer to the problem left open in [RACHŮNEK, J.,SALOUNOV A, D.
Abstract: We prove some fundamental properties of monotone modal operators on bounded commutative integral residuated lattices (CRL). Moreover we give a positive answer to the problem left open in [RACHŮNEK, J.—SALOUNOV A, D.: Modal operators on bounded commutative residuated Rl-monoids, Math. Slovaca 57 (2007), 321–332].
17 citations
01 Jan 1997
TL;DR: This paper presents a new temporal logic, the selective mu-calculus, with the property that only the actions occurring in a formula are relevant to check the formula itself, and proves that it is as powerful as the mu-Calculus.
17 citations
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TL;DR: The semantics of modal categories is broadened, admitting propositions about the possibility of results of experiments, and the usual variant of the logic of quantum mechanics is leaned upon.
Abstract: We lean upon the usual variant of the logic of quantum mechanics [1] Here the propositions correspond to the results of the quantum experiments A beautiful essay [2] may be connected with a conservation of semantics But we try to broaden the semantics, admitting propositions about the possibility of results of experiments Doing so, we fulfil the old wish of W A Fock, who attracts our attention to the importance of the modal categories for the interpretation of the quantum theory [3] ?1 Modal system We begin with the formal description of the modal system Br' The alphabet contains the signs - , v and D1 (negation, alternative and the sign of necessity), the set V of the propositional variables and parentheses The rules of formation are: if A E V, then A is a proposition; if X and Y are propositions, then - X, X v Y and DX are propositions also; there are no other propositions X3 will design the set of all propositions
17 citations
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TL;DR: In this paper, the completeness of the Wl extension of the tense-logic presented by Segerberg is proved for a countable language of ordinary prepositional logic with two modal operators: O ("tomorrow") and D ("always").
Abstract: In his forthcoming examination of G. H. von Wright's tense-logic [4], Krister Segerberg studies certain infinitary extensions of the original tense-logic created by von Wright. For one of these extensions the completeness problem turned out to be harder than was expected at first sight. This paper is devoted to a proof of a completeness theorem for the extension in question, called Wl by Segerberg. We use a countable language of ordinary prepositional logic supplied with two modal operators: O ("tomorrow") and D ("always"). The relevant semantics for tense-logic based on this language uses the frame 9^ = , where the successorrelation is the accessibility-relation for O and n A is true at k. We assume that the reader is familiar with ordinary Kripkesemantics for modal languages and, in particular, that he understands what it means that "9ft is a model on the frame 9^". We shall use O(A] as a shorthand for
17 citations
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TL;DR: A bimodal epistemic logic intended to capture knowledge astruth in all epistemically alternative states and belief as a generalised ‘majority’ quantifier, interpreted as truth in most (i.e. a ‘ majority’) of the epistemical alternative states is introduced.
Abstract: We introduce a bimodal epistemic logic intended to capture knowledge as truth in all epistemically alternative states and belief as a generalised ‘majority’ quantifier, interpreted as truth in most (i.e. a ‘majority’) of the epistemically alternative states. This doxastic interpretation is of interest in knowledge-representation applications and it also holds an independent philosophical and technical appeal. The logic comprises an epistemic modal operator, a doxastic modal operator of consistent and complete belief and ‘bridge’ axioms which relate knowledge to belief. To capture the notion of a ‘majority’ we use the ‘large sets’ introduced independently by K. Schlechta and V. Jauregui, augmented with a requirement of completeness, which furnishes a ‘weak ultrafilter’ concept. We provide semantics in the form of possible-worlds frames, properly blending relational semantics with a version of general Scott–Montague (neighbourhood) frames and we obtain soundness and completeness results. We examine the vali...
17 citations