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

statements which are true in all models are provable. Although the logical consequence relation is only semidecidable, much progress has been made in automated...

thought of as providing accounts of the nature of logical truth, as well as logical consequence. Logical truths are generally considered to be necessarily...

deductive-theoretic and model-theoretic conceptions of logical consequence. Logical consequence, a fundamental concept in logic, is the relation between...

pointing out that his definition of logical consequence depends upon a division of terms into the logical and the extra-logical and he expresses some skepticism...

with the deductive nature of the system. The logical consequence (or entailment) of the system by its logical foundation is what distinguishes a formal system...

deductive argument is usually referred to as "logical consequence". According to Alfred Tarski, logical consequence has 3 essential features: it is necessary...

compactness theorem, demonstrating the finitary nature of first-order logical consequence. These results helped establish first-order logic as the dominant...

then }}\Sigma \vdash \phi } that is, for any statement that is a logical consequence of Σ {\displaystyle \Sigma } there actually exists a deduction of...

In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication...

validity, and logical consequence. While logical syntax concerns the formal rules for constructing well-formed expressions, logical semantics establishes...

is derivable from a set Γ of sentences of that language is also a logical consequence of that set, in the sense that any model that makes all members of...

be expressed more generally in terms of logical consequence. We say that a sentence s is a syntactic consequence of a theory T, denoted T ⊢ s {\displaystyle...

the logical semantics, any result of a computation of a concurrent logic program is a logical consequence of the program, even though not all logical consequences...

effectively determined. A theory (set of sentences closed under logical consequence) in a fixed logical system is decidable if there is an effective method for...

logically equivalent if they have the same truth value in every model. The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes...

Jr. (1996). Logical dilemmas: The life and work of Kurt Gödel. Taylor & Francis. ISBN 978-1-56881-025-6. Dawson, John W. Jr. (1997). Logical dilemmas: The...

{\displaystyle P\rightarrow \bot } (where → {\displaystyle \rightarrow } is logical consequence and ⊥ {\displaystyle \bot } is absolute falsehood). Conversely, one...

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can...

theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms...

for every formula φ in its language, at least one of φ or ¬φ is a logical consequence of the theory. Presburger arithmetic is an axiom system for the natural...

Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference...

\wedge } ) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as ∧ {\displaystyle...

semantics (i.e. what they mean). A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive...

deductive argument asserts that the truth of the conclusion is a logical consequence of the premises: if the premises are true, the conclusion must be...

formal language need not be symbols of anything. For instance there are logical constants which do not refer to any idea, but rather serve as a form of...

argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises...

interpretation that satisfies ψ then φ is said to be a logical consequence of ψ). Some of the logical symbols of a language (other than quantifiers) are truth-functional...

Gregory Bateson introduced a theory of logical types into the social sciences; his notions of double bind and logical levels are based on Russell's theory...

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical...