# Category: Modal logic

Assertoric
An assertoric proposition in Aristotelian logic merely asserts that something is (or is not) the case, in contrast to which assert the possibility of something being true, or apodeictic propositions w
Multimodal logic
A multimodal logic is a modal logic that has more than one primitive modal operator. They find substantial applications in theoretical computer science.
Modal depth
In modal logic, the modal depth of a formula is the deepest nesting of modal operators (commonly and ). Modal formulas without modal operators have a modal depth of zero.
General frame
In logic, general frames (or simply frames) are Kripke frames with an additional structure, which are used to model modal and intermediate logics. The general frame semantics combines the main virtues
Modal fallacy
The formal fallacy of the modal fallacy is a special type of fallacy that occurs in modal logic. It is the fallacy of placing a proposition in the wrong modal scope, most commonly confusing the scope
KK thesis
The KK thesis or KK principle is a principle of epistemic logic which states that "If you know that P is the case then you know that you know that P is the case." This means that one cannot know that
Potentiality and actuality
In philosophy, potentiality and actuality are a pair of closely connected principles which Aristotle used to analyze motion, causality, ethics, and physiology in his Physics, Metaphysics, Nicomachean
Vivid designator
In modal logic and the philosophy of language, a vivid designator is a term which is believed to designate the same thing in all possible worlds and nothing else where such an object does not exist in
Alternating-time temporal logic
In computer science, alternating-time temporal logic, or ATL, is a branching-time temporal logic that extends computation tree logic (CTL) to multiple players. ATL naturally describes computations of
Doxastic logic
Doxastic logic is a type of logic concerned with reasoning about beliefs. The term doxastic derives from the Ancient Greek δόξα (doxa, "opinion, belief"), from which the English term doxa ("popular op
Buridan formula
In quantified modal logic, the Buridan formula and the converse Buridan formula (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers a
Regular modal logic
In modal logic, a regular modal logic is a modal logic containing (as axiom or theorem) the duality of the modal operators: and closed under the rule Every normal modal logic is regular, and every reg
Contingency (philosophy)
In philosophy and logic, contingency is the status of propositions that are neither true under every possible valuation (i.e. tautologies) nor false under every possible valuation (i.e. contradictions
Apodicticity
"Apodictic", also spelled "apodeictic" (Ancient Greek: ἀποδεικτικός, "capable of demonstration"), is an adjectival expression from Aristotelean logic that refers to propositions that are demonstrably,
Japaridze's polymodal logic
Japaridze's polymodal logic (GLP) is a system of provability logic with infinitely many provability modalities. This system has played an important role in some applications of provability algebras in
Modal collapse
In modal logic, modal collapse is the condition in which every true statement is necessarily true, and vice versa; that is to say, there are no contingent truths, or to put it another way, that "every
Normal modal logic
In logic, a normal modal logic is a set L of modal formulas such that L contains: * All propositional tautologies; * All instances of the Kripke schema: and it is closed under: * Detachment rule (m
Free choice inference
Free choice is a phenomenon in natural language where a linguistic disjunction appears to receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the followi
Actualism
In analytic philosophy, actualism is the view that everything there is (i.e., everything that has being, in the broadest sense) is actual. Another phrasing of the thesis is that the domain of unrestri
Simplification of disjunctive antecedents
In formal semantics and philosophical logic, simplification of disjunctive antecedents (SDA) is the phenomenon whereby a disjunction in the antecedent of a conditional appears to distribute over the c
Löb's theorem
In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that "if P is provable in PA then P is true",
Subjunctive possibility
Subjunctive possibility (also called alethic possibility) is a form of modality studied in modal logic. Subjunctive possibilities are the sorts of possibilities considered when conceiving counterfactu
Gabbay's separation theorem
In mathematical logic and computer science, Gabbay's separation theorem, named after Dov Gabbay, states that any arbitrary temporal logic formula can be rewritten in a logically equivalent "past → fut
Dynamic logic (modal logic)
In logic, philosophy, and theoretical computer science, dynamic logic is an extension of modal logic capable of encoding properties of computer programs. A simple example of a statement in dynamic log
Rigid designator
In modal logic and the philosophy of language, a term is said to be a rigid designator or absolute substantial term when it designates (picks out, denotes, refers to) the same thing in all possible wo
Kripke semantics
Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 195
Induction puzzles
Induction puzzles are logic puzzles, which are examples of multi-agent reasoning, where the solution evolves along with the principle of induction. A puzzle's scenario always involves multiple players
Alethic modality
Alethic modality (from Greek ἀλήθεια = truth) is a linguistic modality that indicates modalities of truth, in particular the modalities of logical necessity, contingency, possibility and impossibility
Classical modal logic
In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators that is also closed under the rule Alternatively, one can give a dual d
Autoepistemic logic
The autoepistemic logic is a formal logic for the representation and reasoning of knowledge about knowledge. While propositional logic can only express facts, autoepistemic logic can express knowledge
Epistemic possibility
In philosophy and modal logic, epistemic possibility relates a statement under consideration to the current state of our knowledge about the actual world: a statement is said to be: * epistemically p
Modal companion
In logic, a modal companion of a superintuitionistic (intermediate) logic L is a normal modal logic that interprets L by a certain canonical translation, described below. Modal companions share variou
Standard translation
In modal logic, standard translation is a way of transforming formulas of modal logic into formulas of first-order logic which capture the meaning of the modal formulas. Standard translation is define
Non-rigid designator
In the philosophy of language and modal logic, a term is said to be a non-rigid designator (or flaccid designator) or connotative term if it does not extensionally designate (denote, refer to) the sam
Sahlqvist formula
In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every formula is canonical, and corresponds to a fir
Gödel's ontological proof
Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (10
Modal algebra
In algebra and logic, a modal algebra is a structure such that * is a Boolean algebra, * is a unary operation on A satisfying and for all x, y in A. Modal algebras provide models of propositional mo
Provability logic
Provability 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 for
Interpretability logic
Interpretability logics comprise a family of modal logics that extend provability logic to describe interpretability or various related metamathematical properties and relations such as weak interpret
Essence
Essence (Latin: essentia) is a polysemic term, used in philosophy and theology as a designation for the property or set of properties that make an entity or substance what it fundamentally is, and whi
Epistemic closure
Epistemic closure is a property of some belief systems. It is the principle that if a subject knows , and knows that entails , then can thereby come to know . Most epistemological theories involve a c
Barcan formula
In quantified modal logic, the Barcan formula and the converse Barcan formula (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and
Deontic logic
Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the es
Interior algebra
In abstract algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are to topology and the modal logic S4 w
Modal logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural
Accessibility relation
An accessibility relation is a relation which plays a key role in assigning truth values to sentences in the relational semantics for modal logic. In relational semantics, a modal formula's truth valu
Dynamic epistemic logic
Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge chang
Logical possibility
Logical 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 syste
Two-dimensionalism
Two-dimensionalism is an approach to semantics in analytic philosophy. It is a theory of how to determine the sense and reference of a word and the truth-value of a sentence. It is intended to resolve
Finite model property
In mathematical logic, a logic L has the finite model property (fmp for short) if any non-theorem of L is falsified by some finite model of L. Another way of putting this is to say that L has the fmp
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
Window operator
In modal logic, the window operator is a modal operator with the following semantic definition: for a Kripke model and . Informally, it says that w "sees" every φ-world (or every φ-world is seen by w)
Logico-linguistic modeling
Logico-linguistic modeling is a method for building knowledge-based systems with a learning capability using conceptual models from soft systems methodology, modal predicate logic, and logic programmi
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 logi
Hennessy–Milner logic
In computer science, Hennessy–Milner logic (HML) is a dynamic logic used to specify properties of a labeled transition system (LTS), a structure similar to an automaton. It was introduced in 1980 by M
Neighborhood semantics
Neighborhood semantics, also known as Scott–Montague semantics, is a formal semantics for modal logics. It is a generalization, developed independently by Dana Scott and Richard Montague, of the more
Formal ethics
Formal ethics is a formal logical system for describing and evaluating the "form" as opposed to the "content" of ethical principles. Formal ethics was introduced by Harry J. Gensler, in part in his 19
Predicate abstraction
In logic, predicate abstraction is the result of creating a predicate from a sentence. If Q is any formula then the predicate abstract formed from that sentence is (λy.Q), where λ is an abstraction op
Frege–Church ontology
The Frege–Church ontology is an ontology, a theory of existence. Everything is considered as being in three categories, object (referent, denotation), name, or concept (sense). The ontology was develo
Modal μ-calculus
In theoretical computer science, the modal μ-calculus (Lμ, Lμ, sometimes just μ-calculus, although this can have a more general meaning) is an extension of propositional modal logic (with many modalit
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
In logic, a rule of inference is admissible in a formal system if the set of theorems of the system does not change when that rule is added to the existing rules of the system. In other words, every f
Possible world
A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semant
Deontic modality
Deontic modality (abbreviated DEO) is a linguistic modality that indicates how the world ought to be according to certain norms, expectations, speaker desires, etc. In other words, a deontic expressio
Strict conditional
In logic, a strict conditional (symbol: , or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of c
Guarded logic
Guarded logic is a choice set of dynamic logic involved in choices, where outcomes are limited. A simple example of guarded logic is as follows: if X is true, then Y, else Z can be expressed in dynami
Impossible world
In philosophical logic, the concept of an impossible world (sometimes called a non-normal world)is used to model certainphenomena that cannot be adequately handled using ordinary possible worlds. Anim
Problem of future contingents
Future 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
Fiction theory
Fiction theory is a discipline that applies possible world theory to literature. Fiction theory scholars and critics have articulated various theses rooted in Saul Kripke's application of modal logic
Conceptual necessity
Conceptual necessity is a property of the certainty with which a state of affairs, as presented by a certain description, occurs: it occurs by conceptual necessity if and only if it occurs just by vir
Ontic
In ontology, ontic (from the Greek ὄν, genitive ὄντος: "of that which is") is physical, real, or factual existence. In more nuance, it means that which concerns particular, individuated beings rather
Imperative logic
Imperative logic is the field of logic concerned with imperatives. In contrast to declaratives, it is not clear whether imperatives denote propositions or more generally what role truth and falsity pl
Hybrid logic
Hybrid logic refers to a number of extensions to propositional modal logic with more expressive power, though still less than first-order logic. In formal logic, there; is a trade-off between expressi
Necessity of identity
In modal logic, the necessity of identity is the thesis that for every object x and object y, if x and y are the same object, it is necessary that x and y are the same object. The thesis is best known
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