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.
Papers published on a yearly basis
Papers
More filters
TL;DR: This paper considers some questions related to the determination of epistemic modal domains, and contends that if groups have epistemic states that bear on the modal domain, then careful attention must be paid to the method of combination selected for the epistemicStates of the individuals within the group.
Abstract: This paper considers some questions related to the determination of epistemic modal domains. Specifically, given situations in which groups of agents have epistemic states that bear on a modal domain, how is the domain best restricted? This is a metasemantic project, in which I combine a standard semantics for epistemic modals, as developed by Kratzer, with a standard story about conversational dynamics, as developed by Stalnaker. I show how a standard framework for epistemic logic can model their interaction. I contend that if groups have epistemic states that bear on the modal domain, as the data suggests, then careful attention must be paid to the method of combination selected for the epistemic states of the individuals within the group. Specifically, there should be some explanation of the flow of information in a group-deliberative setting. Through this study we find a novel explanation of modal disagreement and uptake.
2 citations
TL;DR: There is a translation of Lukasiewicz's system into the modal system S5, such that exactly those formulas are theses of threevalued logic whose translator is not without its own peculiarities, however.
Abstract: It is well-known that the intuitions which led Lukasiewicz to propose his system of three-valued logic were modal in character, having to do with the indeterminacy of contingent future tense propositions.' It is also wellknown that the truth-tables for conjunction and negation which he proposes appear to be inconsistent with any such modal interpretation. Specifically, Lukasiewicz adds to the usual values of truth and falsity a third value, intermediate between these two, which he calls "the possible" (but which is more accurately designated "the contingent"). He argues quite plausibly that when a sentence p has this value, its negation Np should also have it. The process by which he arrives at the table for conjunction is not explicitly stated, but in any event, it has the result that the conjunction Kpq is "possible" when both its arguments are.2 The objection is now immediate: although 'Lukasiewicz will be in Warsaw on Friday' and 'Lukasiewicz will not be in Warsaw on Friday' may both (on Monday) be contingent, the same can surely not be said of 'Lukasiewicz will and will not be in Warsaw on Friday', for the latter is always and necessarily false, on Monday as well as every other day. This objection seems so clear and decisive, that it might be (and often has been) supposed that there is no way at all to interpret Lukasiewicz's system modally.3 Surprisingly, however, this turns out not to be the case. On the contrary, we shall see that there is a translation of his system into the modal system S5, such that exactly those formulas are theses of threevalued logic whose translations are theses of S5. The translation is not without its own peculiarities, however.
2 citations
01 Jan 2013
TL;DR: The formalism of cylindric modal logic can be motivated from two directions as discussed by the authors : it forms an interesting bridge over the gap between propositional formalisms and first-order logic, in that it formalizes firstorder logic as if it were a modal formalism: the assignments of firstorder variables can be seen as states or possible worlds of the modality formalism, and the quantifiers ∃ and ∀ may be studied as special cases of modal operators ♢ and ☐, respectively.
Abstract: The formalism of cylindric modal logic can be motivated from two directions. In its own right, it forms an interesting bridge over the gap between propositional formalisms and first-order logic, in that it formalizes first-order logic as if it were a modal formalism: The assignments of first-order variables can be seen as states or possible worlds of the modal formalism, and the quantifiers ∃ and ∀ may be studied as special cases of the modal operators ♢ and ☐, respectively. Elaborating this idea, we find that from this modal viewpoint, the standard semantics of first-order logic corresponds to just one of many possible classes of Kripke frames, and that other classes might be of interest as well.
2 citations
29 Jun 2021
TL;DR: In this article, a geometrical interpretation of the process of constructing the operator ∆ is given, and new additional properties of this operation are formulated and checked, providing an analogue to the De Morgan's Law (Theorem 1), an analogue of the Fixed Point Theorem (theorem 2), the connections between the operation ∆ on one hand and the classical modal operators over IFS Necessity and Possibility, on the other (Theorems 3 and 4).
Abstract: Recently, the new operation ∆ was introduced over intuitionistic fuzzy sets and some of its properties were studied. Here, new additional properties of this operations are formulated and checked, providing an analogue to the De Morgan’s Law (Theorem 1), an analogue of the Fixed Point Theorem (Theorem 2), the connections between the operation ∆ on one hand and the classical modal operators over IFS Necessity and Possibility, on the other (Theorems 3 and 4). It is shown that it can be used for a de-i-fuzzification. A geometrical interpretation of the process of constructing the operator ∆ is given.
2 citations