# Category: Logical consequence

Result
A result (also called upshot) is the final consequence of a sequence of actions or events expressed qualitatively or quantitatively. Possible results include advantage, disadvantage, gain, injury, los
Double turnstile
In logic, the symbol ⊨, ⊧ or is called the double turnstile. It is often read as "entails", "models", "is a semantic consequence of" or "is stronger than". It is closely related to the turnstile symbo
Monotonicity of entailment
Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions. In sequent calculi this propert
Entailment (linguistics)
Linguistic entailments are entailments which arise in natural language. If a sentence A entails a sentence B, sentence A cannot be true without B being true as well. For instance, the English sentence
The paradoxes of material implication are a group of formulae that are intuitively false but treated as true in systems of logic that interpret the conditional connective as material conditional. On t
Theorem
In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the
Rational consequence relation
In logic, a rational consequence relation is a non-monotonic consequence relation satisfying certain properties listed below.
Critical thinking
Critical thinking is the analysis of available facts, evidence, observations, and arguments to form a judgement. The subject is complex; several different definitions exist, which generally include th
Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statem
Deductive closure
In mathematical logic, a set of logical formulae is deductively closed if it contains every formula that can be logically deduced from , formally: if always implies . If is a set of formulae, the dedu
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Therefore sign
In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an
Textual entailment
Textual entailment (TE) in natural language processing is a directional relation between text fragments. The relation holds whenever the truth of one text fragment follows from another text. In the TE
Material conditional
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is tr
Idempotency of entailment
Idempotency of entailment is a property of logical systems that states that one may derive the same consequences from many instances of a hypothesis as from just one. This property can be captured by
Consequent
A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if P implies Q, then P is called the a
Tautological consequence
In propositional logic, tautological consequence is a strict form of logical consequence in which the tautologousness of a proposition is preserved from one line of a proof to the next. Not all logica
Inference
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deductio
Argument
An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three