Provability logicProvability logic is a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as Peano arithmetic. There are a number of provability logics, some of which are covered in the literature mentioned in . The basic system is generally referred to as GL (for Gödel–Löb) or L or K4W (W stands for well-foundedness). It can be obtained by adding the modal version of Löb's theorem to the logic K (or K4).
Accident (philosophy)An accident (Greek συμβεβηκός), in metaphysics and philosophy, is a property that the entity or substance has contingently, without which the substance can still retain its identity. An accident does not affect its essence. It does not mean an "accident" as used in common speech, a chance incident, normally harmful. Examples of accidents are color, taste, movement, and stagnation. Accident is contrasted with essence: a designation for the property or set of properties that make an entity or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity.
IndexicalityIn semiotics, linguistics, anthropology, and philosophy of language, indexicality is the phenomenon of a sign pointing to (or indexing) some element in the context in which it occurs. A sign that signifies indexically is called an index or, in philosophy, an indexical. The modern concept originates in the semiotic theory of Charles Sanders Peirce, in which indexicality is one of the three fundamental sign modalities by which a sign relates to its referent (the others being iconicity and symbolism).
Logical possibilityLogical possibility refers to a logical proposition that cannot be disproved, using the axioms and rules of a given system of logic. The logical possibility of a proposition will depend upon the system of logic being considered, rather than on the violation of any single rule. Some systems of logic restrict inferences from inconsistent propositions or even allow for true contradictions. Other logical systems have more than two truth-values instead of a binary of such values.
Problem of future contingentsFuture contingent propositions (or simply, future contingents) are statements about states of affairs in the future that are contingent: neither necessarily true nor necessarily false. The problem of future contingents seems to have been first discussed by Aristotle in chapter 9 of his On Interpretation (De Interpretatione), using the famous sea-battle example. Roughly a generation later, Diodorus Cronus from the Megarian school of philosophy stated a version of the problem in his notorious master argument.
Linear temporal logicIn logic, linear temporal logic or linear-time temporal logic (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode formulae about the future of paths, e.g., a condition will eventually be true, a condition will be true until another fact becomes true, etc. It is a fragment of the more complex CTL*, which additionally allows branching time and quantifiers. LTL is sometimes called propositional temporal logic, abbreviated PTL.
Metaphysical necessityIn philosophy, metaphysical necessity, sometimes called broad logical necessity, is one of many different kinds of necessity, which sits between logical necessity and nomological (or physical) necessity, in the sense that logical necessity entails metaphysical necessity, but not vice versa, and metaphysical necessity entails physical necessity, but not vice versa. A proposition is said to be necessary if it could not have failed to be the case.
