into logical symbols and non-logical symbols (sometimes also called logical and non-logical constants). The non-logical symbols of a language of first-order...

symbols Logic alphabet, a suggested set of logical symbols Logic gate § Symbols Logical connective Mathematical operators and symbols in Unicode Non-logical...

the extension { ( a ) } {\displaystyle \{(\mathrm {a} )\}} to the non-logical symbol T {\displaystyle T} , and does not make a claim about whether T {\displaystyle...

In logic, a logical constant or constant symbol of a language L {\displaystyle {\mathcal {L}}} is a symbol that has the same semantic value under every...

the relation denoted by R {\displaystyle R} . Since predicates are non-logical symbols, they can denote different relations depending on the interpretation...

and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather...

unambiguous symbols. This allows logical statements to not be understood in an ambiguous way. These symbols are called logical connectives, logical operators...

especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature lists the...

then there is a formula ρ, called an interpolant, such that every non-logical symbol in ρ occurs both in φ and ψ, φ implies ρ, and ρ implies ψ. The theorem...

formal fallacy is a pattern of reasoning rendered invalid by a flaw in its logical structure. Propositional logic, for example, is concerned with the meanings...

rarely used, see List of logic symbols. ¬    (not sign) Denotes logical negation, and is read as "not". If E is a logical predicate, ¬ E {\displaystyle...

A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern.[citation...

Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that...

Non-logical axioms may also be called "postulates", "assumptions" or "proper axioms". In most cases, a non-logical axiom is simply a formal logical expression...

if it is ℵα-saturated. The countable random graph, with the only non-logical symbol being the edge existence relation, is also saturated, because any...

logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as...

used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different...

the symbol ¬ {\displaystyle \neg } signifies logical negation, ∨ {\displaystyle \lor } signifies OR, and ∧ {\displaystyle \land } signifies AND. Non-disjunction...

mathematical, logical, and set notation. The Supplemental Mathematical Operators block (U+2A00–U+2AFF) contains various mathematical symbols, including N-ary...

disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs...

In mathematical logic and computer science the symbol ⊢ ( ⊢ {\displaystyle \vdash } ) has taken the name turnstile because of its resemblance to a typical...

often not clear how to distinguish formal from non-formal features, i.e. logical from non-logical symbols. This distinction lies at the very heart of the...

Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth...

other non-logical symbols, and a formula is said to be satisfiable if there is some interpretation which makes it true. While this allows non-standard...

called metatheorems. A logical system is a deductive system (most commonly first order logic) together with additional non-logical axioms. According to...

arithmetic. Just as in first-order logic, second-order logic may include non-logical symbols in a particular second-order language. These are restricted, however...

sentence that is a string of symbols consisting of logical symbols v1...vn representing logical connectives, and non-logical symbols c1...cn, then if and only...

{\displaystyle \mathbb {N} .} The non-logical symbols for the axioms consist of a constant symbol 0 and a unary function symbol S. The first axiom states that...

A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output...

construct different models of logical consequence and logical truth. Philosophical logic is understood to encompass and focus on non-classical logics, although...