# Category: Non-classical logic

SQLf
SQLf is a SQL extended with fuzzy set theory application for expressing flexible (fuzzy) queries to traditional (or ″Regular″) Relational Databases. Among the known extensions proposed to SQL, at the
Quantum logic
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The f
Relevance logic
Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substr
The World of Null-A
The World of Null-A, sometimes written The World of Ā, is a 1948 science fiction novel by Canadian-American writer A. E. van Vogt. It was originally published as a three-part serial in 1945 in Astound
Dialetheism
Dialetheism (from Greek δι- di- 'twice' and ἀλήθεια alḗtheia 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true stat
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
Connexive logic
Connexive logic names one class of alternative, or non-classical, logics designed to exclude the paradoxes of material implication. The characteristic that separates connexive logic from other non-cla
Probabilistic logic network
A probabilistic logic network (PLN) is a conceptual, mathematical, and computational approach to uncertain inference; inspired by logic programming, but using probabilities in place of crisp (true/fal
Subjective logic
Subjective logic is a type of probabilistic logic that explicitly takes epistemic uncertainty and source trust into account. In general, subjective logic is suitable for modeling and analysing situati
The Temperature Paradox or Partee's Paradox is a classic puzzle in formal semantics and philosophical logic. Formulated by Barbara Partee in the 1970s, it consists of the following argument, which spe
Infinitary logic
An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Some infinitary logics may have different properties from those of standard first-order logic. In p
Substructural logic
In logic, a substructural logic is a logic lacking one of the usual structural rules (e.g. of classical and intuitionistic logic), such as weakening, contraction, exchange or associativity. Two of the
Default logic
Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions. Default logic can express facts like “by default, something is true”; by contrast, st
Combs method
The Combs method is a rule base reduction method of writing fuzzy logic rules described by in 1997. It is designed to prevent combinatorial explosion in fuzzy logic rules. The Combs method takes advan
Rational consequence relation
In logic, a rational consequence relation is a non-monotonic consequence relation satisfying certain properties listed below.
EL++
EL++ is a lightweight description logic that was designed to * capture the expressive power that is used by large-scale ontologies from practical applications * have polytime reasoning problems, in
Defeasible logic
Defeasible logic is a non-monotonic logic proposed by to formalize defeasible reasoning. In defeasible logic, there are three different types of propositions: strict rulesspecify that a fact is always
Cirquent calculus
Cirquent calculus is a proof calculus that manipulates graph-style constructs termed cirquents, as opposed to the traditional tree-style objects such as formulas or sequents. Cirquents come in a varie
Non-monotonic logic
A non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences (cf. defeasible reas
Journal of Applied Non-Classical Logics
Journal of Applied Non-Classical Logics is a peer reviewed academic journal published by Taylor & Francis. It focusses on non-classical logic, in particular formal aspects (completeness, decidability,
Probabilistic logic
Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic trut
Free logic
A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty
Intensional logic
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe (extensions), by additional quantifiers that ran
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
Computability logic
Computability logic (CoL) is a research program and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed to classical logic which is a formal theory
Description logic
Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic. In contrast to the
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
Circumscription (logic)
Circumscription is a non-monotonic logic created by John McCarthy to formalize the common sense assumption that things are as expected unless otherwise specified. Circumscription was later used by McC
Inquisitive semantics
Inquisitive semantics is a framework in logic and natural language semantics. In inquisitive semantics, the semantic content of a sentence captures both the information that the sentence conveys and t
Schrödinger logic
Schrödinger logics are a kind of non-classical logic in which the law of identity is restricted. These logics are motivated by the consideration that in quantum mechanics, elementary particles may be
Plausible reasoning
Plausible reasoning is a method of deriving new conclusions from given known premises, a method different from the classical syllogistic argumentation methods of Aristotelian two-valued logic. The syl
Minimal logic
Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson. It is an intuitionistic and paraconsistent logic, that rejects both the law of the excluded
Rvachev function
In mathematics, an R-function, or Rvachev function, is a real-valued function whose sign does not change if none of the signs of its arguments change; that is, its sign is determined solely by the sig
Non-classical logic
Non-classical logics (and sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several w
Alternative semantics
Alternative semantics (or Hamblin semantics) is a framework in formal semantics and logic. In alternative semantics, expressions denote alternative sets, understood as sets of objects of the same sema
Trivialism
Trivialism is the logical theory that all statements (also known as propositions) are true and that all contradictions of the form "p and not p" (e.g. the ball is red and not red) are true. In accorda
Linear logic
Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties o
Nixon diamond
In nonmonotonic reasoning, the Nixon diamond is a scenario in which default assumptions lead to mutually inconsistent conclusions. The scenario is: * usually, Quakers are pacifist * usually, Republi
Paraconsistent logic
A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studyi
Noneism
Noneism, also known as modal Meinongianism (named after Alexius Meinong), is a theory in logic and metaphysics. It holds that some things do not exist. It was first coined by Richard Routley in 1980 a
Independence-friendly logic
Independence-friendly logic (IF logic; proposed by Jaakko Hintikka and in 1989) is an extension of classical first-order logic (FOL) by means of slashed quantifiers of the form and , where is a finite
Intermediate logic
In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent superintuitionistic logic; thus, consistent supe
Deviant logic
Deviant logic is a type of logic incompatible with classical logic. Philosopher Susan Haack uses the term deviant logic to describe certain non-classical systems of logic. In these logics: * the set
Intuitionistic logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion
Fuzzy concept
A fuzzy concept is a kind of concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. This means the concept is
Material inference
In logic, inference is the process of deriving logical conclusions from premises known or assumed to be true. In checking a logical inference for formal and material validity, the meaning of only its
Preferential entailment
Preferential entailment is a non-monotonic logic based on selecting only models that are considered the most plausible. The plausibility of models is expressed by an ordering among models called a pre
Fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value ma
Dynamic semantics
Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sente