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Modal operator information


A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of being non-truth-functional in the following sense: The truth-value of composite formulae sometimes depend on factors other than the actual truth-value of their components. In the case of alethic modal logic, a modal operator can be said to be truth-functional in another sense, namely, that of being sensitive only to the distribution of truth-values across possible worlds, actual or not. Finally, a modal operator is "intuitively" characterized by expressing a modal attitude (such as necessity, possibility, belief, or knowledge) about the proposition to which the operator is applied.[1]

  1. ^ Garson, James (2021). "Modal Logic". The Stanford Encyclopedia of Philosophy (Summer 2021 ed.). Metaphysics Research Lab, Stanford University. Retrieved 5 February 2024.

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Modal operator

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A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general...

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tautology in deontic modal logic, since what ought to be true can be false. Modal logics are formal systems that include unary operators such as ◊ {\displaystyle...

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De dicto and de re

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existential quantifiers are within the scope of the modal operator, whereas in de re claims the modal operator falls within the scope of the existential quantifier...

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Epistemic modal logic

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Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition...

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(media) in a single artifact Multimodal logic modal logic that has more than one primitive modal operator Evolutionary multimodal optimization, finding...

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logical symbols Logic gate § Symbols Logical connective Mathematical operators and symbols in Unicode Non-logical symbol Polish notation Truth function...

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Deontic logic

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are multiple agents involved in the domain of discourse, the deontic modal operator can be specified to each agent to express their individual obligations...

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Epistemic modality

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illocutionary operators, such as the assertion operator, question operator or imperative operator. According to him this explains why most epistemic modals in English...

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Modal adjective

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following examples with the modal adjective in bold. Here the modal adjective is analyzed semantically as a sentential modal operator. It's possible that some...

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Interior algebra

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interior algebra. The interior operator in this case corresponds to the modal operator □ (necessarily), while the closure operator corresponds to ◊ (possibly)...

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Strict conditional

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{\displaystyle \Box } , or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material...

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Predicate abstraction

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two cases: (i) when t is irreferential and (ii) when Q contains modal operators. In modal logic the "de re / de dicto distinction" is stated as 1. (DE DICTO):...

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Logical connective

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Dialetheism Four-valued logic List of Boolean algebra topics Logical constant Modal operator Propositional calculus Term logic Tetralemma Truth function Truth table...

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Multimodal transport

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which consists of more than 100 universities nationwide conducts multi-modal research and education programs. The European Commission has invested heavily...

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denotes a set of beliefs. In doxastic logic, belief is treated as a modal operator. There is complete parallelism between a person who believes propositions...

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and ¬ {\displaystyle \neg } ), and the modal operator ◻ {\displaystyle \Box } ("necessarily"). The modal operator ◊ {\displaystyle \Diamond } ("possibly")...

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Free choice inference

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receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to...

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Interpretability logic

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propositional logic by adding the unary modal operator ◻ {\displaystyle \Box } and the binary modal operator ▹ {\displaystyle \triangleright } (as always...

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English modal auxiliary verbs

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Look up Appendix:English modal verbs in Wiktionary, the free dictionary. The English modal auxiliary verbs are a subset of the English auxiliary verbs...

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Multimodal logic

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logic is a modal logic that has more than one primitive modal operator. They find substantial applications in theoretical computer science. A modal logic with...

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In modal logic, the window operator △ {\displaystyle \triangle } is a modal operator with the following semantic definition: M , w ⊨ △ ϕ ⟺ ∀ u , M , u...

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Truth function

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Boolean-valued function List of Boolean algebra topics Logical constant Modal operator Propositional calculus Truth-functional propositional logic Roy T. Cook...

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Metric temporal logic

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the temporal modal operator UI (pronounced "φ until in I ψ."), with I an interval of non-negative numbers. the temporal modal operator SI (pronounced...

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Intensional logic

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'into' modal contexts. The operators appear in the grammar as sentential functors, they are called modal operators. As mentioned, precursors of modal logic...

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