A universal proposition in logic.

(logic) the property of two operations x and y, such that ax(ayb) = a, and ay(axb) = a

(logic) The branch of logic dealing with truth and error.

(logic) The "inclusive or" truth function.

(logic) The binary operator and, only true if both of two inputs is true. In infix notation.

(electronics) a logic gate performing a Boolean logic AND operation

Alternative spelling of ansatz [(mathematics) A mathematical assumption used to describe a certain phenomenon, posited in order to help provisionally solve an equation or other problem.]

(mathematics) The first term of a ratio, i.e. the term a in the ratio a:b, the other being the consequent.

(computing) The logic governing what a computer program is trying to accomplish; domain logic.

(logic) The result of replacing parts of an argument with letters, leaving only logic words such as "if" and "for all" unreplaced.

(logic) Alternative form of argument form [(logic) The result of replacing parts of an argument with letters, leaving only logic words such as "if" and "for all" unreplaced.]

(logic) A hierarchy which classifies the complexity of first-order formulae (and sets defined by them) based on the number of alternations between series of unbounded existential quantifiers and universal quantifiers.

(Lojban grammar) the number of arguments (in Lojban grammar called sumti) specified in the definition of a selbri. (the selbri combined with the sumti make up a bridi).

(databases) A set of references (or, more precisely, inference rules) used to infer all the functional dependencies on a relational database.

(logic, of a proposition) Lacking logical operators; unable to be made simpler in logical form.

(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that two sets are equal if and only if they contain the same elements.

(set theory) One of the axioms in axiomatic set theory that guarantees the existence of an infinite set.

(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that if two sets exist, there exists a set with those two sets as its sole elements.

(set theory) One of the axioms in axiomatic set theory, equivalent to the statement that a union exists for any set, containing exactly all the elements contained within the sets within that set.

(logic) A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.

(logic) A formula in the language of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.

(logic) A set of axioms from which theorems can be derived.

(computing) A formal notation for context-free grammars.

(logic) In quantified modal logic, the formula ∀x□Fx→□∀xFx, meaning "if every x is necessarily F, then it is necessary that every x is F".

(logic) an equivalence relation between state transition systems, associating systems which behave in the same way in the sense that one system simulates the other and vice-versa

(programming) A Boolean variable, one whose value is either true or false.

(logic, computing) A variable that can hold a single true/false (1/0) value.

(algebra, logic, computing) Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT

(logic) A logical proposition that cannot be derived from other logical propositions by a Boolean operation.

(algebra, logic, computing) Any function based on the operations AND, OR and NOT, and whose elements are from the domain of Boolean algebra

(mathematics, logic, computing) A system of symbolic logic that is the basis of Boolean algebra

(mathematics, logic, computing) Any variable, from the domain of Boolean algebra, having one of only two values

(logic) In quantified modal logic, the formula Diamond ∀xFx→∀x Diamond Fx, meaning "if possibly everything is F, then everything is possibly F".

(computing) Algorithms in a software system that models real life business objects and their interactions.

(logic) Conjunctive normal form with the additional property that all of the terms of the product contain the same literals, so that the terms differ from each other only in their patterns of complementation (of their literals).

(logic) Disjunctive normal form with the additional property that all of the terms of the sum contain the same literals, so that the terms differ from each other only in their patterns of complementation (of their literals).

(computing) The process of solving new problems based on the known solutions of similar problems encountered in the past.

(logic) A categorical proposition.

(logic) A proposition that asserts or denies that members of one category (the subject term) belong to another (the predicate term). There are four types: "all S are P", "all S are not P", "some S are P", and "some S are not P".

(logic) A kind of logic based on the principles that each proposition has a truth value of either "true" or "false", but not both, and that if a proposition were to be both true and false or neither true nor false then a result would be that all propositions would be both true and false.

(logic) Synonym of conjunctive normal form

(logic) The process of converting logic statements into standard clauses.

(logic) A method, algorithm or program that converts logic statements into standard clauses.

(logic) A formula which has no free occurrences of variables; or equivalently, in which all occurrences of variables are bound.

Alternative spelling of coinduction [(logic) A form of induction that allows some form of reasoning concerning sets that are not well founded; uses a form of relation called a bisimulation]

(logic, of a set of propositions) mutually alternate

(logic) A form of induction that allows some form of reasoning concerning sets that are not well founded; uses a form of relation called a bisimulation

(computer science) Model of computation based on combinators.

(logic, game theory) A special kind of knowledge for a group of agents, such that when all the agents in a group G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum.

(computing) a binary operator that tests for equality or inequality and evaluates to true or false

(logic) An expression related to some other expression such that it is true under the same conditions that make other false, and vice versa.

(logic, of a proof system of a formal system with respect to a given semantics) In which every semantically valid well-formed formula is provable.

(computing, mathematics) a formal theory of computability

(logic) Recursion theory.

(computer science) A particular modal logic of branching time with operators "next", "globally", "finally" or "eventually", "until", and "weak until".

(programming) synonym of ternary operator

(logic) Either term of a conjunction.

(logic) The proposition resulting from the combination of two or more propositions using the ∧ ( and ) operator.

(logic) A conjunction.

(logic) The form of a boolean formula that the formula has if the formula is a conjunction of disjunctions of literals, such as “(A or B or C) and (D or E or not F)”.

(logic) A function that operates on truth values to give another truth value.

(logic) The following theorem of Boolean algebra: XY+X'Z+YZ=XY+X'Z where YZ, the algebraically redundant term, is called the "consensus term", or its dual form (X+Y)(X'+Z)(Y+Z)=(X+Y)(X'+Z), in which case Y+Z is the consensus term. (Note: X+Y,X'+Z⊢Y+Z is an example of the resolution inference rule (replacing the + with ∨ and the prime with prefix ¬ might make this more evident).)

(mathematics, logic) An extension of a logical theory such that every theorem expressible in the original theory is also derivable within the original theory.

(logic) Freedom from contradiction; the state of a system of axioms such that none of the propositions deduced from them are mutually contradictory.

(logic) Of a set of statements: such that no contradiction logically follows from them.

(logic) Any kind of logic in which any proof of existence can be converted into an algorithm that constructs the mathematical object which it claims to exist.

(logic) For a formula: a finite set of variables, which set contains all the free variables in the given formula.

(logic, countable) A statement which is neither a tautology nor a contradiction.

A rule stating that the use of prior probabilities of 0 or 1 should be avoided, except when applied to statements that are logically true or false, so as to leave room for the possibility that something very unlikely is in fact the case.

(logic) An algorithm for checking the validity of a first-order logic formula using a resolution-based decision procedure for propositional logic.

(mathematics, loosely) Any of various laws similar to De Morgan’s laws for set theory and logic; for example: ¬∀𝑥 𝑃(𝑥) ⇔ ∃𝑥 ¬𝑃(𝑥)

(logic) in intuitionistic logic, a proposition P is decidable in a given theory if it can be proven from the theory that "either P or not P", i.e. in symbols: P∨¬P.

(logic) A procedure for "discharging" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form P,A⊢C to an inference of the form P⊢A→C or vice versa, where ⊢ is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory.

(logic, countable) A specific such representation.

(logic) A Horn clause with exactly one positive literal.

(logic) The number of logical connectives in a formula.

(logic) A formal system capturing the concepts of obligation and permission.

(logic) the number of simple elements which an abstract conception or notion includes; the comprehension or content

(logic) One of a family of knowledge representation languages which can be used to represent the concept definitions of an application domain (known as terminological knowledge) in a structured and formally well-understood way.

Any formal system of reasoning that arrives at a truth by the exchange of logical arguments.

(logic circuits) A Boolean operation which is true when the two input variables are different but is otherwise false; the XOR operation ( scriptstyle A◌̅B+◌̅AB).

(electronics) a logic gate whose output is TRUE when the two inputs are different; a Boolean logic XOR gate.

(logic) One of multiple propositions, any of which, if true, confirm the validity of another proposition (a disjunction).

(mathematics) A logical operator that results in “true” when some of its operands are true.

(logic) Of or related to a disjunction.

(logic) The form of a boolean formula that the formula has if the formula is a disjunction of conjunctions of literals, such as “(A and B and C) or (D and E and not F)”.

(logic) A logical argument of the form that if there are only two possibilities, and one of them is ruled out, then the other must take place. In symbols: P∨Q,¬P⊢Q

(logic) Assigning the species of a general term.

(computing) A more general name for business logic. (The logic could run in an organisation that is not a business.)

(logic) In predicate logic, an indication of the relevant set of entities that are being dealt with by quantifiers.

(logic, model theory) The ⊨ symbol used to denote semantic consequence, or the ⊨ symbol used to denote the fact that the model to the left of it satisfies the set of sentences to its right.

(logic) A type of modal logic which deals with statements involving beliefs.

(logic) A relation between two structures which have the property that every first-order formula is valid in one structure if and only if it is valid in the other.

(logic) The act of obtaining by separation, or as the result of eliminating; deduction.

(programming, informal) A binary operator that returns its first operand if that operand evaluates to true, and otherwise evaluates and returns its second operand.

(mathematics, logic) A decision problem of finding a way to decide whether a formula is true or provable within a given system.

The logic function exclusive OR (as opposed to inclusive OR), whose output is true only when exactly one of its inputs is true.

(mathematics) An instance of reasoning performed using this approach.

(logic, of each of two statements) able to be deduced from the other

(logic, of two formulas) The condition of being equisatisfiable.

(logic) Of a pair of formulas, where one formula is satisfiable whenever the other is satisfiable (either both formulas are satisfiable or both are not).

(mathematics) A Boolean operation that is TRUE when both input variables are TRUE or both input variables are FALSE, but otherwise FALSE; the XNOR function.

(electronics) a logic gate performing a Boolean logic equivalence operation; an XNOR gate.

(mathematics) Relating to the corresponding elements of an equivalence relation.

(logic) A disjunction which is true if only one, but not both, of its disjuncts is true.

(logic, computing) An exclusive disjunction; the result of applying the above-described exclusive or to two or more predicates; contrasted with an inclusive or, which is the result of applying an inclusive or.

Alternative spelling of exclusive or [(logic, computing) Exclusive disjunction: the use of or to indicate that of two predicates, one is true and one is false (without specifying which is which); contrasted with inclusive or, which does not imply that one must be false.]

(logic) In predicate logic, an inference rule of the form ∃x P(x) ⊢ P(c), where c is a new symbol (not part of the original domain of discourse, but which can stand for an element of it (as in Skolemization)).

(logic) The operator, represented by the symbol ∃, used in predicate calculus to indicate that a predicate is true for at least one member of a specified set. Verbal equivalents include "there exists" and "there is".

(logic) Either the logical law ((P∧Q)→R)⇒(P→(Q→R)), or the rule of replacement ((P∧Q)→R)⇔(P→(Q→R)).

(logic) The set of tuples of values that, used as arguments, satisfy the predicate.

(electronics) one of two states of a Boolean variable; logic 0.

(definite, mathematics) the requirements for an object to be considered a field:

(logic) The form of a syllogism with respect to the relative position of the middle term.

(informal) Reasoning, logic.

(logic) Pertaining to finite-length proofs, each using a finite set of axioms.

(mathematics, logic) Of one of a series of models, languages, relationship, forms of logical discourse, etc., being the simplest one or the first in a sequence.

(logic) A formal deductive system extended from propositional logic with the possibility to quantify over individuals of the domain of discourse.

(logic, computer science) Initialism of first-order logic. [(logic) A formal deductive system extended from propositional logic with the possibility to quantify over individuals of the domain of discourse.]

(logic) Initialism of first-order logic. [(logic) A formal deductive system extended from propositional logic with the possibility to quantify over individuals of the domain of discourse.]

(logic) A particular logical calculus.

A study that is concerned with theoretical formal systems, such as logic, mathematics, systems theory and the theoretical branches of computer science, information theory, microeconomics, statistics, and linguistics.

(logic) The grouping of a formal language and a set of inference rules and/or axioms.

(logic) An argument's property of being valid due to being an instance of an argument form.

(logic) Any of a set of rules used to construct well-formed formulas of a formal language.

(logic) A syntactic expression of a proposition, built up from quantifiers, logical connectives, variables, relation and operation symbols, and, depending on the type of logic, possibly other operators such as modal, temporal, deontic or epistemic ones.

A three-bit computational circuit that swaps the last two bits if the first bit is 1. Any logical or arithmetic operation can be constructed entirely of such gates.

A theorem stating that, if we have free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles.

(mathematics) A form of reasoning, derived from fuzzy set theory, whereby a truth value need not be exactly zero (false) or one (true), but rather can be zero, one, or any value in between.

(logic, mathematics) One of two theorems in mathematical logic that demonstrates the inherent limitations of every formal axiomatic system containing basic arithmetic.

(logic) The set of all ground terms that may be formed (even recursively) using any of the constants and functions which appear in a given set of formulae. (If there is no constant in that given set of formulae, then designate one default constant as being usable for the aforementioned purpose.)

(logic) The conversion of a formula of first-order logic which involves the following steps: (1) replace free variables with constants, (2) replace any variable bound by a universal quantifier which lies in the scope of an even number of logical negations with a Herbrand function, and (3) replace any variable bound by an existential quantifier which lies in the scope of an odd number of negations with a Herbrand function.

(logic) The branch of logic concerned with discovery or invention

(computing theory) A formal system of rules for reasoning about the correctness of computer programs, based on Hoare triples, which describe the state of the system before and after various operations.

(computing theory) A formal description of how the execution of a piece of code changes the state of the computation in Hoare logic, consisting of a command to be run, a precondition that holds true beforehand, and a postcondition that holds true afterwards.

(logic) A clause (disjunction of literals) with at most one positive literal.

(logic) The symbol ⊃.

(countable, logic) The connective in propositional calculus that, when joining two predicates A and B in that order, has the meaning "if A is true, then B is true".

(logic) A minimalist version of propositional calculus which uses only the logical connectives → ("implies") and ⊥ ("false").

(logic) The logical law (P→(Q→R))⇒((P∧Q)→R).

(logic, of a proposition) definable only in terms of a totality of which it is itself a part

(logic) A disjunction which is true if at least one of its disjuncts is true.

(logic, computing) A logical connective joining two or more predicates that yields the logical value "true" when at least one of the predicates is true.

(mathematics) A method of proof of a theorem by first proving it for a specific case (often an integer; usually 0 or 1) and showing that, if it is true for one case then it must be true for the next.

(logic, proof theory) A rule for combining (or modifying) well-formed formulas of a formal language in a truth-preserving manner (to yield new well-formed formulas).

Abbreviation of infinite. [Something that is infinite in nature.]

That branch of logic whose task is to develop non-formal standards, criteria, procedures for the analysis, interpretation, evaluation, criticism and construction of argumentation in everyday discourse.

(logic) A formal deductive system able to represent the distinction between intension and extension of a term.

(logic, philosophy) That can be defined in terms of each other.

(countable, logic, model theory) An assignment of a truth value to each propositional symbol of a propositional calculus.

(mathematics, logic) Dealing strictly in constructive proofs, abstaining from proof by contradiction

(mathematics, logic) A type of logic which rejects the axiom law of excluded middle or, equivalently, the law of double negation and/or Peirce's law. It is the foundation of intuitionism.

(Boolean algebra) A tabular representation of the possible results of a logical expression

(logic) A set, whose elements are called nodes or worlds, together with a preordering relation for that set, called its accessibility relation.

(logic) A Kripke frame together with either one of the following: (1) a function associating each of the frame's worlds to a set of prime formulae which are "true" for the given world, (2) a function associating each prime formula to a set of worlds for which the prime formula is "true", (3) a forcing relation between worlds and prime formulae. Additionally, there is a set of rules for deducing (from the given function or relation) what formulae are forced to be true by a given world. (The set of rules depends on which logic the Kripke model is being applied to, whether one of several modal logics or intuitionistic logic).

(logic) The statement that the negation of the negation of A implies A, for any proposition A. Stated symbolically: ¬¬A→A.

(logic) A logical principle which states all statements must be either true or false, i.e. in symbols: P∨¬P.

(logic) The logical principle that anything equals itself, expressed by the symbolic equation A=A.

(logic) The rule that states that not all propositions are true, the opposite of trivialism.

Alternative form of law of excluded middle [(logic) A logical principle which states all statements must be either true or false, i.e. in symbols: P∨¬P.]

(philosophy) The identity of indiscernibles.

(logic) Law of excluded middle.

(logic) A logic in which two structural rules are missing from its sequent calculus: those for weakening and contraction; which has some extra logical connectives, so that it has both "additive" and "multiplicative" versions of the typical binary connectives and truth constants; and which has a pair of modal, "exponential" operators for resource management, to help make up for the loss of the two structural rules.

(logic) A propositional variable or the negation of a propositional variable. ᵂᵖ

(uncountable) A method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved. Logic is the basis of many principles including the scientific method.

a chain of multiple logic gates

(programming) Programming with a paradigm that bases on formal logic

(computing) Relating to the conceptual model of a system rather than its physical expression

(logic) A formal system.

(logic) A truth-valued function such as (the usual suspects): conjunction, disjunction, negation, and material implication.

(logic) A word or phrase which has an invariant logical meaning and which is useful for forming argument forms.

(logic) A formal system.

(philosophy) The doctrine that mathematics is a branch of logic in that some or all mathematics is reducible to logic.

logicalness

Obsolete spelling of logic [(uncountable) A method of human thought that involves thinking in a linear, step-by-step manner about how a problem can be solved. Logic is the basis of many principles including the scientific method.]

(logic) A theorem stating that, in any formal system F with Peano arithmetic, for any formula P, if it is provable in F that "if P is provable in F then P is true", then P is provable in F.

(logic) A logic that directly supports classification of entities into disjunct sorts.

(logic) A kind of non-classical propositional calculus whose semantics makes use of more than two truth values.

The branch of logic that focuses on the content of reasoning.

(mathematics) A method of proof which, in terms of a predicate P, could be stated as: if P(0) is true and if for any natural number n>0, P(n) implies P(n+1), then P(n) is true for any natural number n.

(logic) A subfield of logic and mathematics consisting of both the mathematical study of logic and the application of this study to other areas of mathematics, exemplified by questions on the expressive power of formal logics and the deductive power of formal proof systems.

(logic) Said of a set of well-formed formulas: that it is as large as it can be without being inconsistent; i.e. that for any well-formed formula φ, the set contains either φ or ~φ.

(logic, philosophy) The use of inductive reasoning to select the best choice from a number of different methods of prediction.

(logic) A statement about theorems proven in a metalanguage.

(logic) A modal proposition.

(logic) Any formal system that attempts to deal with modalities, such as possibility and necessity, but also obligation and permission.

(logic) The classification of propositions on the basis on whether they claim possibility, impossibility, contingency or necessity; mode.

(logic) An interpretation function which assigns a truth value to each atomic proposition.

(logic) The fragment of predicate logic in which all predicate letters are monadic (that is, they take only one argument), and there are no function letters.

(logic) A formal deductive system which extends first-order logic by the ability to quantify over unary predicates over individual members of the universe of discourse.

(logic) Relating to, or expressed as a monosyllogism

(Boolean algebra) A Boolean function with the property that switching any one input variable from 0 to 1 results either in no change in output or a change from 0 to 1.

(logic) modus tollens

(logic, probability theory) Describing multiple events or propositions such that the occurrence of any one implies the nonoccurrence of all other events or propositions.

(logic) A binary operator composite of NOT AND; negation of AND function.

(electronics) a logic gate performing a Boolean logic NAND operation

A kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning, in contrast to axiomatic systems.

(logic) The logical operation which obtains such (negated) propositions.

(logic) Of or relating to a general form of logic in which each proposition has separate values for truth, falsehood, and indeterminacy.

(statistics, of a variable) Having values whose order is insignificant.

A logic that is not classical: one that extends or deviates from classical logic.

(logic, electronics) Alternative form of NOR [A binary operator composite of NOT OR; negation of OR function.]

(electronics) a logic gate performing a Boolean logic NOR operation

(mathematics, logic) A unary operation on logical values that changes true to false, and false to true.

A relation symbol that indicates that two expressions are different; the ≠ symbol.

(logic, mathematics) A function that is equivalent to the NOT operator.

(electronics) a logic gate performing a Boolean-logic NOT operation

(mathematics, logic) An operation on logical values that changes true to false, and false to true.

(computing theory) Both NP-easy and NP-hard.

(logic, of a modality) That is necessarily or absolutely different than the respective coordinate alethic or temporal modality, but not its opposite.

(logic) A logical system involving theory of classes, developed by Stanislaw Lesniewski (1886-1939).

(logic) The binary operator inclusive or, true if one at least one of two inputs is true. In infix notation.

(electronics) a logic gate performing a Boolean logic OR operation

(logic, uncountable) The study of such systems.

(logic, rare) Conversion to a paraconsistent form.

(logic) A technique for reasoning on sets of clauses where the predicate symbol is equality.

(logic) A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, addition and multiplication, including a first-order schema of induction.

(logic) The classically valid but intuitionistically non-valid formula ((P→Q)→P)→P of propositional calculus, which can be used as a substitute for the law of excluded middle in implicational propositional calculus.

S and T are disjoint, i.e. no object can be both a place and a transition

(logic) A logical system or fragment thereof not containing a negation operator.

(mathematics) The probability that a hypothesis is true (calculated by Bayes' theorem).

(logic) The process of making a statement more precise.

(logic) One of the five most general relations of attributes involved in logical arrangements, namely, genus, species, difference, property, and accident.

(computing) An operator or function that returns either true or false.

(logic) The branch of logic that deals with quantified statements such as "there exists an x such that..." or "for any x, it is the case that...", where x is a member of the domain of discourse.

(logic) First-order logic.

(computing) The parallel execution of all possible outcomes of a branch instruction, all except one of which are discarded after the branch condition has been evaluated.

(mathematics, logic) Part at the beginning of a prenex formula where all of the formula's bound variables get bound by logical quantifiers.

(logic) A way of expressing a formula of predicate logic such the formula consists of a prenex and a matrix, with the prenex preceding the matrix.

(logic) A set of axioms of first-order logic for the natural numbers specifying the operations of zero, successor, and addition, including a first-order schema of induction, without multiplication.

(computing) The logic that is concerned with how domain/business objects are displayed to users of the software.

(logic) A well-formed formula which has not been made by combining simpler well-formed formulas by means of logical connectives.

(logic) A set of axioms and a set of inference rules which are jointly used to deduce tautologies, thereby providing proofs of them.

(logic) propositional logic.

(logic) One of a set of letters or symbols which are assigned fixed truth values independently of any interpretation or valuation, and each of which qualifies as a prime formula of their language.

(logic) An expression containing algebraic symbols that serve to represent words or other elements of a sentence or proposition

(logic) A formal deductive system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives.

(logic) A variable that can either be true or false.

(computing) The transformation of a relational dataset into a propositional one.

(logic) A limitation that is imposed on the variables of a proposition.

(logic) An operator, such as the universal quantifier (written as ∀) or the existential quantifier (∃), used in predicate calculus to indicate the degree that predicate is true for a specified set.

(logic) To relate a statement (called a predicate) to a given set using a quantifier—either for all (denoted ∀) or there exists (denoted ∃).

(logic, quantum mechanics) A set of events that is closed under a countable disjunction of countably many mutually exclusive events.ᵂᴾ

(Internet) The number of comments to a post or other expression on social media relative to the number of likes; a high ratio suggests disagreement with the contents of the original post.

(databases) A database model that is based on first-order predicate logic.

(computing) synonym of comparison operator

(logic, philosophy) A term that is related to the referent

A kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related, and aiming to capture aspects of implication that are ignored by the "material implication" operator in classical truth-functional logic.

(logic, computer science) a wide range of potentially non-deterministic methods of replacing subterms of a formula with other terms

The paradox where, given the observation that certain English phrases unambiguously define real numbers while others do not, there is an infinitely long list of English phrases that unambiguously define real numbers, yet (using a similar technique to Cantor's diagonal argument) it is possible to generate another such phrase not in the list.

(cellular automata) An elementary cellular automaton based on the exclusive-or function.

(logic) A formula in the metalanguage of an axiomatic system, in which one or more schematic variables appear, which stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.

(logic) A variable that appears in an axiom schema and ranges over formulas, distinguished from the variables of the axiom schema that are quantified over and that range over the individuals of the universe of discourse.

(logic) The shortest sub-wff of which a given instance of a logical connective is a part.

A formal system which extends first-order logic by allowing quantification over relations between members of the universe.

(logic) A truth tree.

(logic) propositional logic

(logic) A disjunctive set of logical formulae which is partitioned into two subsets; the first subset, called the antecedent, consists of formulae which are valuated as false, and the second subset, called the succedent, consists of formulae which are valuated as true. (The set is written without set brackets and the separation between the two subsets is denoted by a turnstile symbol, which may be read "give(s)".)

(mathematics, logic) A set of inference rules for deriving true sequents from other true sequents.

(logic, uncountable) The act of representing one logic or language with another by providing a syntactic translation.

(logic) The vertical bar symbol | denoting the NAND operation.

(computing) A logical operator that returns a value as soon as the outcome is certain, without necessarily testing all operands (for example, an OR operator returning true if the first operand evaluates as true, without evaluating the second operand).

Alternative spelling of short circuit operator [(computing) A logical operator that returns a value as soon as the outcome is certain, without necessarily testing all operands (for example, an OR operator returning true if the first operand evaluates as true, without evaluating the second operand).]

A mathematical formalism developed in the 1980s for the representation of meaning or semantics.

(logic) A function which replaces a variable bound by an existential quantifier which lies in the scope of an even number of logical negations; such function is a function of the remaining bound variables whose scope contain the given variable (being replaced).

(logic) The conversion of a formula of first-order logic which involves the following steps: (1) replace free variables with constants, (2) replace any variable bound by an existential quantifier which lies in the scope of an even number of logical negations with a Skolem function, and (3) replace any variable bound by a universal quantifier which lies in the scope of an odd number of negations with a Skolem function.

(logic, computer science) Initialism of second-order logic. [A formal system which extends first-order logic by allowing quantification over relations between members of the universe.]

(logic) The property of a logical theory that whenever a wff is a theorem then it must also be valid. Symbolically, letting T represent a theory within logic L, this can be represented as the property that whenever T⊢𝜙 is true, then T vDash 𝜙 must also be true, for any wff φ of logic L.

(mathematics, logic) Having a wide range of logical consequences; widely applicable. (Often contrasted with a weak statement which it implies.)

(mathematics, logic) A property satisfied by structural translations from sequents into equations or from equations into sequents.

(logic) A set along with a collection of finitary functions and relations.

(logic) A formula that is part of another formula.

(mathematics) A statement proven for use in the proof of a more important statement, usually a lemma

(logic) a functor which takes as input one or more sentences and outputs a term.

(philosophy, mathematics) A proposition making up part of a greater proposition.

(philosophy) A logical relationship in which two terms can be mutually substituted without affecting the truth value of any propositions in which the terms occur, thereby establishing that the terms are identical.

(logic) A statement P in relation to statement Q such that P implies Q.

(Lojban grammar) a parameter ("place") in a selbri (“predicate”)'s "place structure", which can be filled with an argument (sumti (“argument”) in the above sense)

(logic) Describing an extended form of intuitionistic logic

(logic) The relation of a universal proposition to a specific proposition of the same form with the universal quantified variable replaced by a specific instance.

(logic) The relation of a universal proposition to a particular proposition in the same terms.

(logic) A kind of relation between predicates.

(logic) A semantics for dealing with irreferential singular terms and vagueness.

two-element Boolean algebra

(logic) Synonym of Boolean function

(logic) A formal system of deductive logic in which aspects and relationships of natural language are represented by a system of symbols.

(fuzzy logic) Any kind of fuzzy logic whose semantics valuates conjunctions by means of t-norms.

(countable, logic, propositional logic) A statement that is true for all truth values of its propositional variables.

A form of symbolic logic used to reason about properties of statements related to order and duration.

(logic) The subject or the predicate of a proposition; one of the three component parts of a syllogism, each one of which is used twice.

(logic) An approach to logic that splits propositions into two terms—subject and predicate.

A system of mathematical logic in which there are three truth values.

(logic) A syntactically correct expression that is deducible from the given axioms of a deductive system.

(countable, logic) A set of axioms together with all statements derivable from them; or, a set of statements which are deductively closed. Equivalently, a formal language plus a set of axioms (from which can then be derived theorems). The statements may be required to all be bound (i.e., to have no free variables).

(logic) The character used to represent negation, usually ~ or ¬.

A three-bit computational circuit that inverts the third bit if the first two bits are set, or in other cases leaves all bits unchanged.

(logic) Particularly in the discipline of artificial intelligence, a form of inference, according to which the response appropriate to a particular known case, also is appropriate to another particular case diagnosed to be functionally identical. This contrasts with induction, in which general rules derived from past observations are applied to future cases as a class (compare also analogy).

(logic) An argument containing three alternatives, jointly exhaustive either under any condition(s) or under all condition(s) consistent with the universe of discourse of that argument, that each imply the same conclusion.

(electronics) one of two states of a Boolean variable; logic 1.

Allowing only the answers "true" or "false".

(mathematics, logic) A Boolean function whose value is interpreted as truth or falsity

(logic) A table showing all possible truth values for an expression, derived from the truth values of its components.

(logic) A variation of a truth table in which any node (representing a statement) has branches if and only if other statements (true or false) may be derived from it

(logic) A value indicating to what extent a statement is true; in classical logic, these are the values "true" and "false".

(programming) Evaluating to true in a Boolean context.

(mathematics, logic) The ⊢ symbol used to represent logical entailment (deducibility relation), especially of the syntactic type; i.e., syntactic consequence. (Such symbol can be read as "prove(s)" or "give(s)". )

(logic, of a modality) That is necessarily or absolutely different than the respective coordinate alethic or temporal modality as well as its opposite.

(logic) A conditional-like structure expressing that the consequent holds true regardless of the particular value of the antecedent.

(mathematical logic, computer science) Given two terms, their join with respect to a specialisation order.

(logic) The operator, represented by the symbol ∀, used in predicate calculus to indicate that a predicate is true for all members of a specified set.

(logic) The set of all entities over which quantifiers—including "for all" and "there exists"—range.

(logic) A value equal to 1 minus the truth value of a statement.

(logic) Of a formula or system: such that it evaluates to true regardless of the input values.

(logic, first-order logic, model theory) A structure, and the corresponding assignment of a truth value to each sentence in the language for that structure.

(logic) A function which assigns a truth value to every well-formed formula, which is identical to the model's interpretation function when applied to atomic propositions, and which otherwise assigns a truth value recursively depending on the formula's top logical connective and the truth values of the subformulae surrounding that logical connective.

(logic) The ∨ symbol used to represent the inclusive or, which is a logical connective.

(logic) Having multiple valid solutions.

(mathematics, logic) Having a narrow range of logical consequences; narrowly applicable. (Often contrasted with a strong statement which implies it.)

(uncountable, mathematics) A structural principle of mathematical logic that states that the hypotheses of any derived fact may be freely extended with additional assumptions.

(logic) A statement that is expressed in a valid, syntactically correct, manner.

Acronym of well-formed formula. [(logic) A statement that is expressed in a valid, syntactically correct, manner.]

(electrical engineering, rare) XNOR, a logic gate.

(electrical engineering, rare) XOR, a logic gate

(electrical engineering) A logic gate which is the inverse of XOR.

(electronics) a logic gate performing a Boolean logic XNOR operation; an equivalence gate

The logic function exclusive OR (as opposed to inclusive OR), whose output is true only when exactly one of its inputs is true.

(electronics) a logic gate performing a Boolean logic XOR operation

(logic) Describing situations in which the veracity of a statement may be shown to be true without revealing any other information.

propositional logic

(mathematics, fuzzy logic) An approach to transforming a fuzzy membership function into a basic belief assignment.