Functional completeness
In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expressio
Satisfiability modulo theories
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable. It generalizes the Boolean satisfiability
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
Operational semantics
Operational semantics is a category of formal programming language semantics in which certain desired properties of a program, such as correctness, safety or security, are verified by constructing pro
Typed lambda calculus
A typed lambda calculus is a typed formalism that uses the lambda-symbol to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to
Boolean flag
A Boolean flag, truth bit or truth flag in computer science is a Boolean value represented as one or more bits, which encodes a state variable with two possible values.
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
State space enumeration
In computer science, state space enumeration are methods that consider each reachable program state to determine whether a program satisfies a given property. As programs increase in size and complexi
Formal verification
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal spe
Combinational logic
In automata theory, combinational logic (also referred to as time-independent logic or combinatorial logic ) is a type of digital logic which is implemented by Boolean circuits, where the output is a
WalkSAT
In computer science, GSAT and WalkSAT are local search algorithms to solve Boolean satisfiability problems. Both algorithms work on formulae in Boolean logic that are in, or have been converted into c
Runtime verification
Runtime verification is a computing system analysis and execution approach based on extracting information from a running system and using it to detect and possibly react to observed behaviors satisfy
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-
Herbrand Award
The Herbrand Award for Distinguished Contributions to Automated Reasoning is an award given by the Conference on Automated Deduction (CADE), Inc., (although it predates the formal incorporation of CAD
Logic optimization
Logic optimization is a process of finding an equivalent representation of the specified logic circuit under one or more specified constraints. This process is a part of a logic synthesis applied in d
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.
Boolean satisfiability problem
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if
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
Forward chaining
Forward chaining (or forward reasoning) is one of the two main methods of reasoning when using an inference engine and can be described logically as repeated application of modus ponens. Forward chain
Horn-satisfiability
In formal logic, Horn-satisfiability, or HORNSAT, is the problem of deciding whether a given set of propositional Horn clauses is satisfiable or not. Horn-satisfiability and Horn clauses are named aft
HOL (proof assistant)
HOL (Higher Order Logic) denotes a family of interactive theorem proving systems using similar (higher-order) logics and implementation strategies. Systems in this family follow the LCF approach as th
OBJ (programming language)
OBJ is a programming language family introduced by Joseph Goguen in 1976, and further worked on by Jose Meseguer.
SAT solver
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem. On input a formula over Boolean variables, such as "(x or y) and (x o
Geometry of interaction
The Geometry of Interaction (GoI) was introduced by Jean-Yves Girard shortly after his work on linear logic. In linear logic, proofs can be seen as various kinds of networks as opposed to the flat tre
Assertion (software development)
In computer programming, specifically when using the imperative programming paradigm, an assertion is a predicate (a Boolean-valued function over the state space, usually expressed as a logical propos
Intuitionistic type theory
Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics.Intuitionistic type theory was created by P
Q0 (mathematical logic)
Q0 is Peter Andrews' formulation of the simply-typed lambda calculus,and provides a foundation for mathematics comparable to first-order logic plus set theory.It is a form of higher-order logic and cl
Undecidable problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a corre
Sequential logic
In automata theory, sequential logic is a type of logic circuit whose output depends on the present value of its input signals and on the sequence of past inputs, the input history. This is in contras
Stuttering equivalence
In theoretical computer science, stuttering equivalence, a relation written as , can be seen as a partitioning of path and into blocks, so that states in the block of one path are labeled the same as
Abstract rewriting system
In mathematical logic and theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviated ARS) is a formalism that captures the qui
Multi-Agent Programming Contest
The Multi-Agent Programming Contest is an annual international programming competition with stated goal of stimulating research in the area of multi-agent system development and programming.
Structural induction
Structural induction is a proof method that is used in mathematical logic (e.g., in the proof of Łoś' theorem), computer science, graph theory, and some other mathematical fields. It is a generalizati
Rewriting
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known
Event calculus
The event calculus is a logical language for representing and reasoning about events and their effects first presented by Robert Kowalski and in 1986. It was extended by Murray Shanahan and in the 199
Model elimination
Model Elimination is the name attached to a pair of proof procedures invented by Donald W. Loveland, the first of which was published in 1968 in the Journal of the ACM. Their primary purpose is to car
Computation tree logic
Computation tree logic (CTL) is a branching-time logic, meaning that its model of time is a tree-like structure in which the future is not determined; there are different paths in the future, any one
Karnaugh map
The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which was a redis
Successor function
In mathematics, the successor function or successor operation sends a natural number to the next one. The successor function is denoted by S, so S(n) = n + 1. For example, S(1) = 2 and S(2) = 3. The s
Ordered weighted averaging aggregation operator
In applied mathematics – specifically in fuzzy logic – the ordered weighted averaging (OWA) operators provide a parameterized class of mean type aggregation operators. They were introduced by Ronald R
Axiomatic semantics
Axiomatic semantics is an approach based on mathematical logic for proving the correctness of computer programs. It is closely related to Hoare logic. Axiomatic semantics define the meaning of a comma
Büchi arithmetic
Büchi arithmetic of base k is the first-order theory of the natural numbers with addition and the function which is defined as the largest power of k dividing x, named in honor of the Swiss mathematic
Journal of Automated Reasoning
The Journal of Automated Reasoning was established in 1983 by Larry Wos, who was its editor in chief until 1992. It covers research and advances in automated reasoning, mechanical verification of theo
Unification (computer science)
In logic and computer science, unification is an algorithmic process of solving equations between symbolic expressions. Depending on which expressions (also called terms) are allowed to occur in an eq
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
Type-1 OWA operators
Type-1 OWA operators are a set of aggregation operators that generalise the Yager's OWA (ordered weighted averaging) operators) in the interest of aggregating fuzzy sets rather than crisp values in so
Horn clause
In mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form which gives it useful properties for use in logic programming, formal specification, and
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
Precondition
In computer programming, a precondition is a condition or predicate that must always be true just prior to the execution of some section of code or before an operation in a formal specification. If a
Separation logic
In computer science, separation logic is an extension of Hoare logic, a way of reasoning about programs.It was developed by John C. Reynolds, Peter O'Hearn, Samin Ishtiaq and Hongseok Yang, drawing up
Twelf
Twelf is an implementation of the logical framework LF developed by Frank Pfenning and Carsten Schürmann at Carnegie Mellon University. It is used for logic programming and for the formalization of pr
Postcondition
In computer programming, a postcondition is a condition or predicate that must always be true just after the execution of some section of code or after an operation in a formal specification. Postcond
Perceptual computing
Perceptual computing is an application of Zadeh's theory of computing with words on the field of assisting people to make subjective judgments.
Logic for Computable Functions
Logic for Computable Functions (LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators in early 1970s, based on the theoretical foundatio
Type-2 fuzzy sets and systems
Type-2 fuzzy sets and systems generalize standard Type-1 fuzzy sets and systems so that more uncertainty can be handled. From the beginning of fuzzy sets, criticism was made about the fact that the me
Semantics (computer science)
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language
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
Bunched logic
Bunched logic is a variety of substructural logic proposed by Peter O'Hearn and . Bunched logic provides primitives for reasoning about resource composition, which aid in the compositional analysis of
Normal form (abstract rewriting)
In abstract rewriting, an object is in normal form if it cannot be rewritten any further, i.e. it is irreducible. Depending on the rewriting system, an object may rewrite to several normal forms or no
Tseytin transformation
The Tseytin transformation, alternatively written Tseitin transformation, takes as input an arbitrary combinatorial logic circuit and produces a boolean formula in conjunctive normal form (CNF), which
Logic in computer science
Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas:
* Theoretical foundations and analysi
Proof complexity
In logic and theoretical computer science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational resources
Presburger arithmetic
Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Mojżesz Presburger, who introduced it in 1929. The signature of Presburger arithmetic contains o
Star-free language
A regular language is said to be star-free if it can be described by a regular expression constructed from the letters of the alphabet, the empty set symbol, all boolean operators – including compleme
Noise-based logic
Noise-based logic (NBL) is a class of multivalued deterministic logic schemes, developed in the twenty-first century, where the logic values and bits are represented by different realizations of a sto
Denotational semantics
In computer science, denotational semantics (initially known as mathematical semantics or Scott–Strachey semantics) is an approach of formalizing the meanings of programming languages by constructing
Model checking
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically as
Journal of Logic and Computation
The Journal of Logic and Computation is a peer-reviewed academic journal focused on logic and computing. It was established in 1990 and is published by Oxford University Press under licence from Profe
Functional verification
In electronic design automation, functional verification is the task of verifying that the logic design conforms to specification. Functional verification attempts to answer the question "Does this pr
Computational logic
Computational logic is the use of logic to perform or reason about computation. It bears a similar relationship to computer science and engineering as mathematical logic bears to mathematics and as ph
Combinatory logic
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in compu
DiVincenzo's criteria
The DiVincenzo criteria are conditions necessary for constructing a quantum computer, conditions proposed in 2000 by the theoretical physicist David P. DiVincenzo, as being those necessary to construc
Logical Methods in Computer Science
Logical Methods in Computer Science (LMCS) is a peer-reviewed open access scientific journal covering theoretical computer science and applied logic. It opened to submissions on September 1, 2004. The
Boolean circuit
In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean c
Logical framework
In logic, a logical framework provides a means to define (or present) a logic as a signature in a higher-order type theory in such a way that provability of a formula in the original logic reduces to
CompCert
CompCert is a formally verified optimizing compiler for a large subset of the C99 programming language (known as Clight) which currently targets PowerPC, ARM, RISC-V, x86 and x86-64 architectures. Thi
Game semantics
Game semantics (German: dialogische Logik, translated as dialogical logic) is an approach to formal semantics that grounds the concepts of truth or validity on game-theoretic concepts, such as the exi
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
Maximum satisfiability problem
In computational complexity theory, the maximum satisfiability problem (MAX-SAT) is the problem of determining the maximum number of clauses, of a given Boolean formula in conjunctive normal form, tha
Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giusepp
Bisimulation
In theoretical computer science a bisimulation is a binary relation between state transition systems, associating systems that behave in the same way in that one system simulates the other and vice ve
CTL*
CTL* is a superset of computational tree logic (CTL) and linear temporal logic (LTL). It freely combines path quantifiers and temporal operators. Like CTL, CTL* is a branching-time logic. The formal s
Frege system
In proof complexity, a Frege system is a propositional proof system whose proofs are sequences of formulas derived using a finite set of sound and implicationally complete inference rules. Frege syste
Interference freedom
In computer science, interference freedom is a technique for proving partial correctness ofconcurrent programs with shared variables. Hoare logic had been introduced earlierto prove correctness of seq
Race condition
A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable eve
Racetrack problem
A racetrack problem is a specific instance of a type of race condition. A racetrack problem is a flaw in a system or process whereby the output and/or result of the process is unexpectedly and critica
Backward chaining
Backward chaining (or backward reasoning) is an inference method described colloquially as working backward from the goal. It is used in automated theorem provers, inference engines, proof assistants,
Algebraic semantics (computer science)
In computer science, algebraic semantics is a form of axiomatic semantics based on algebraic laws for describing and reasoning about program specifications in a formal manner.
Dershowitz–Manna ordering
In mathematics, the Dershowitz–Manna ordering is a well-founded ordering on multisets named after Nachum Dershowitz and Zohar Manna. It is often used in context of termination of programs or term rewr
Knowledge Interchange Format
Knowledge Interchange Format (KIF) is a computer language designed to enable systems to share and re-use information from knowledge-based systems. KIF is similar to frame languages such as KL-One and
Automated reasoning
In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of a
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
Symposium on Logic in Computer Science
The ACM–IEEE Symposium on Logic in Computer Science (LICS) is an annual academic conference on the theory and practice of computer science in relation to mathematical logic. Extended versions of selec
Decidable sublanguages of set theory
In mathematical logic, various sublanguages of set theory are decidable. These include:
* Sets with Monotone, Additive, and Multiplicative Functions.
* Sets with restricted quantifiers.
Anti-unification (computer science)
Anti-unification is the process of constructing a generalization common to two given symbolic expressions. As in unification, several frameworks are distinguished depending on which expressions (also
ACM Transactions on Computational Logic
ACM Transactions on Computational Logic (ACM TOCL) is a scientific journal that aims to disseminate the latest findings of note in the field of logic in computer science. It is published by the Associ
Fluent (artificial intelligence)
In artificial intelligence, a fluent is a condition that can change over time. In logical approaches to reasoning about actions, fluents can be represented in first-order logic by predicates having an
ΛProlog
λProlog, also written lambda Prolog, is a logic programming language featuring polymorphic typing, modular programming, and higher-order programming. These extensions to Prolog are derived from the hi