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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

Marquand diagram

No description available.

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

Veitch chart

No description available.

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

Weakest precondition

No description available.

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

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