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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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TL;DR: In this paper, the authors study logics with a modal operator Kw for knowing whether a proposition is true or false, and show that logic cannot define many common frame properties and its expressive power less than that of basic modal logic over classes of models without reflexivity.
Abstract: Knowing whether a proposition is true means knowing that it is true or knowing that it is false In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that This logic is not a normal modal logic, because we do not have Kw (phi -> psi) -> (Kw phi -> Kw psi) Knowing whether logic cannot define many common frame properties, and its expressive power less than that of basic modal logic over classes of models without reflexivity These features make axiomatizing knowing whether logics non-trivial We axiomatize knowing whether logic over various frame classes We also present an extension of knowing whether logic with public announcement operators and we give corresponding reduction axioms for that We compare our work in detail to two recent similar proposals
1 citations
Journal Article•
TL;DR: The addition of a modal operator in the language of classical relevant logic and the axioms φ ∧ ψ → (φ ∇ ψ) → ( φ∧ ψ�) do not necessarily produce theorems such that as (π�→ ψ→ φ) → φ → ψ or (♦φ→ψ)→ (δά⩽)
Abstract: R. Meyer and E. Mares [10] studied the logic CNR, a classical relevant logic with a modal connective. Such logic is of type S4. As it has been noted in [10], the addition of a modal operator in the language of classical relevant logic and the axioms φ ∧ ψ → (φ ∧ ψ) and (φ ∧ ψ) → ( φ ∧ ψ) do not necessarily produce theorems such that as (φ→ ψ) → φ → ψ or (♦φ→ ψ) → (φ→ ψ). These formulas are well known theorems of classical modal logic [9]. We will define here classical relevant algebras with a modal operator. We shall investigate some types of algebras
1 citations
01 Jul 2011
TL;DR: 9th International Workshop on Nonmonotonic Reasoning, Action and Change (NRAC 2011), Barcelona, Spain, 16-17 July 2011
Abstract: 9th International Workshop on Nonmonotonic Reasoning, Action and Change (NRAC 2011), Barcelona, Spain, 16-17 July 2011
1 citations
1 citations
Journal Article•
TL;DR: In this paper, an ontology-based first-order modal semantics is proposed, in which ontologies are introduced to restrain the modal logic frames and models, and the assignments of each variable in different possible worlds must conform with the relation S. This approach can correctly characterize the connections among the denotations of each variables in different worlds.
Abstract: First-order modal logic is not just propositional modal logic plus classical quantifier machinery. The situation is much subtler than that. The addition of quantifiers to propositional modal logic may lead to many difficulties. In this paper we aim to solve one of them - the problem of rigidity versus non-rigidity for variables, that is, how to determine the denotations for each variable in different possible worlds or the connections among the denotations of each variable in different possible worlds. Since all the currently proposed semantics for first-order modal logic are not suitable to solve this problem, we proposed an ontology-based first-order modal semantics, in which ontologies are introduced to restrain the modal logic frames and models. An ontology-based counterpart relation S is introduced into each model. By requiring that the assignments of each variable in different possible worlds must accord with the relation S, we can correctly characterize the connections among the denotations of each variable in different worlds.
1 citations