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
Ω-logic
In set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure . Jus
Categorical logic
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also notable for its connections to theoretical co
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
Propositional calculus
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions
Frege's propositional calculus
In mathematical logic, Frege's propositional calculus was the first axiomatization of propositional calculus. It was invented by Gottlob Frege, who also invented predicate calculus, in 1879 as part of
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
Many-sorted logic
Many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects, but to partition it in a way that is similar to types in typeful programming. Bo
Dependence logic
Dependence logic is a logical formalism, created by Jouko Väänänen, which adds dependence atoms to the language of first-order logic. A dependence atom is an expression of the form , where are terms,
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
Discourse representation theory
In formal linguistics, discourse representation theory (DRT) is a framework for exploring meaning under a formal semantics approach. One of the main differences between DRT-style approaches and tradit
Higher-order logic
In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logi
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
Aṣṭādhyāyī
The Aṣṭādhyāyī (Sanskrit: अष्टाध्यायी, Aṣṭādhyāyī) is a grammar that describes a form of early Indo-Aryan: Sanskrit. Authored by Sanskrit philologist and scholar Pāṇini and dated to around 500 BCE, it
Propositional proof system
In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for proving classical propositional tautologies.
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
Second-order logic
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and
Zeroth-order logic
Zeroth-order logic is first-order logic without variables or quantifiers. Some authors use the phrase "zeroth-order logic" as a synonym for the propositional calculus, but an alternative definition ex
Logics for computability
Logics for computability are formulations of logic whichcapture some aspect of computability as a basic notion. This usually involves a mixof special logical connectives as well as semantics which exp
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
Ordinal logic
In mathematics, ordinal logic is a logic associated with an ordinal number by recursively adding elements to a sequence of previous logics. The concept was introduced in 1938 by Alan Turing in his PhD
Attributional calculus
Attributional calculus is a logic and representation system defined by Ryszard S. Michalski. It combines elements of predicate logic, propositional calculus, and multi-valued logic. Attributional calc
Implicational propositional calculus
In mathematical logic, the implicational propositional calculus is a version of classical propositional calculus which uses only one connective, called implication or conditional. In formulas, this bi
Type theory
In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories se
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
Systems of Logic Based on Ordinals
Systems of Logic Based on Ordinals was the PhD dissertation of the mathematician Alan Turing. Turing's thesis is not about a new type of formal logic, nor was he interested in so-called ‘ranked logic’
Epsilon calculus
Hilbert's epsilon calculus is an extension of a formal language by the epsilon operator, where the epsilon operator substitutes for quantifiers in that language as a method leading to a proof of consi
Two-variable logic
In mathematical logic and computer science, two-variable logic is the fragment of first-order logic where formulae can be written using only two different variables. This fragment is usually studied w
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
List of Hilbert systems
This article contains a list of sample Hilbert-style deductive systems for propositional logics.
First-order logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer
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