Modal operator

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. See also Garson, James, "Modal Logic", The Stanford Encyclopedia of Philosophy (Summer 2021 Edition), Edward N. Zalta (ed.), URL = The syntax rules for modal operators and are very similar to those for universal and existential quantifiers; In fact, any formula with modal operators and , and the usual logical connectives in propositional calculus () can be rewritten to a de dicto normal form, similar to prenex normal form. One major caveat: Whereas the universal and existential quantifiers only binds to the propositional variables or the predicate variables following the quantifiers, since the modal operators and quantifies over accessible possible worlds, they will bind to any formula in their scope. For example, is logically equivalent to , but is not logically equivalent to ; Instead, is logically equivalent to . When there are both modal operators and quantifiers in a formula, different order of an adjacent pair of modal operator and quantifier can lead to different semantic meanings; Also, when multimodal logic is involved, different order of an adjacent pair of modal operators can also lead to different semantic meanings. There are several ways to interpret modal operators in modal logic, including at least: alethic, deontic, axiological, epistemic, and doxastic.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (4)

Related courses (2)

Related lectures (6)

AR-365: Theory and architectural culture

Le cours offre un résumé de la théorie et la culture architecturales depuis 1789 dans le monde occidentale. Le but est de comprendre des textes dans lesquels l'architecture est définie comme une disci

AR-366: Theory and architectural culture: exercises

Le cours offre une méthode pour discerner et comprendre les idées, les théories et les valeurs culturelles dans des bâtiments et des projets d'architecture.

Modal and Tonal Music

Explores modal and tonal music, analyzing popular music examples like the Beatles' 'Norwegian Wood' to understand scales, tonics, and modes.

Architecture and Society: Innovations, Critique, and Resistance AR-365: Theory and architectural culture

Explores the role of architecture and architects in modern society, questioning if architects can shape society or if architecture is determined by social, political, and economic conditions.

StateSpace Controllability ME-321: Control systems + TP

Explores controllability in state-space models, state transformations, and their impact on state gain.

Modal operator

Epistemic modal logic

Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields, including philosophy, theoretical computer science, artificial intelligence, economics and linguistics. While philosophers since Aristotle have discussed modal logic, and Medieval philosophers such as Avicenna, Ockham, and Duns Scotus developed many of their observations, it was C.

Modal logic

Modal logic is a kind of logic used to represent statements about necessity and possibility. It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation. For instance, in epistemic modal logic, the formula can be used to represent the statement that is known. In deontic modal logic, that same formula can represent that is a moral obligation. Modal logic considers the inferences that modal statements give rise to.