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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.
S5 (modal logic) In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies, and inference ...
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.
In logic, a normal modal logic is a set L of modal formulas such that L contains: and it is closed under: Necessitation rule: implies . The smallest logic satisfying the above conditions is called K. Most modal logics commonly used nowadays (in terms of having philosophical motivations), e.g. C. I. Lewis 's S4 and S5, are normal (and hence are ...
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content.
In logic, contingency is the feature of a statement making it neither necessary nor impossible. [1] [2] Contingency is a fundamental concept of modal logic. Modal logic concerns the manner, or mode, in which statements are true. Contingency is one of three basic modes alongside necessity and possibility. In modal logic, a contingent statement ...
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.
C. I. Lewis. Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. [5] First a noted logician, he later branched into epistemology, and during the last 20 years of his life ...