Knowra Modal logic Modal logic Modal logic is a family of formal systems that extends classical logic with operators for necessity, possibility, knowledge, or time. Its systems differ in which inferences they permit about these modalities.
Possible-world semantics : An approach that evaluates modal claims relative to worlds and relations among them. It interprets necessity across all accessible worlds and possibility across at least one.
Modal operator : A logical operator that expresses a modality, such as necessity or possibility. Modal operators are the distinctive additions to the classical propositional language.
Epistemic logic : A modal logic for representing knowledge and, in some systems, belief. Its operators treat what an agent knows as true across epistemically accessible worlds.
S4 (modal logic) : A normal modal logic extending S4 with axioms T and 4. Its reflexive, transitive frames contrast with weaker systems that omit one or both principles.
Aristotle : An ancient Greek philosopher whose works shaped logic, metaphysics, and natural philosophy. His treatment of necessity and possibility established central problems for later modal theories.
Kripke frame : A set of worlds equipped with a binary accessibility relation. The frame’s relation determines which worlds count when evaluating modal claims.
Necessity : A modality expressing that a proposition must be true under a relevant interpretation. The box operator conventionally formalizes necessity in normal modal logic.
Temporal logic : A family of logics for expressing properties of time, change, and sequences of states. Temporal operators turn modal reasoning toward what holds now, later, or always.
S5 (modal logic) : A modal logic whose standard frames have an equivalence relation as accessibility. S5 validates stronger principles about possibility than K or S4.
C. I. Lewis : An American philosopher who developed influential systems of strict implication and modal logic. His early twentieth-century systems helped establish modern symbolic modal logic.
Show all 28