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2. Sentence (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Sentence_(mathematical_logic)

   Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.

3. Three-valued logic - Wikipedia

   en.wikipedia.org/wiki/Three-valued_logic

   The logic of here and there (HT, also referred as Smetanov logic SmT or as Gödel G3 logic), introduced by Heyting in 1930 [21] as a model for studying intuitionistic logic, is a three-valued intermediate logic where the third truth value NF (not false) has the semantics of a proposition that can be intuitionistically proven to not be false ...

4. Logical consequence - Wikipedia

   en.wikipedia.org/wiki/Logical_consequence

   The Polish logician Alfred Tarski identified three features of an adequate characterization of entailment: (1) The logical consequence relation relies on the logical form of the sentences: (2) The relation is a priori, i.e., it can be determined with or without regard to empirical evidence (sense experience); and (3) The logical consequence ...

5. Logical reasoning - Wikipedia

   en.wikipedia.org/wiki/Logical_reasoning

   Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water ...

6. Propositional calculus - Wikipedia

   en.wikipedia.org/wiki/Propositional_calculus

   Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.

7. Categorical proposition - Wikipedia

   en.wikipedia.org/wiki/Categorical_proposition

   In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term). [1]