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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. 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 ...

  4. Glossary of logic - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_logic

    Logical connectives defined using Kleene's three-valued logic, which includes a third truth value (undefined or unknown) in addition to true and false, accommodating indeterminate propositions. [172] knaves In logic puzzles, individuals who always lie. Used in scenarios like the island of knights and knaves to explore logical deduction. knights

  5. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.

  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. Logic form - Wikipedia

    en.wikipedia.org/wiki/Logic_form

    Logic forms are simple, first-order logic knowledge representations of natural language sentences formed by the conjunction of concept predicates related through shared arguments. Each noun, verb, adjective, adverb, pronoun, preposition and conjunction generates a predicate.

  8. Valuation (logic) - Wikipedia

    en.wikipedia.org/wiki/Valuation_(logic)

    In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema. Valuations are also called truth assignments. In propositional logic, there are no quantifiers, and formulas are built from propositional variables using logical connectives.

  9. Logic - Wikipedia

    en.wikipedia.org/wiki/Logic

    Logic is traditionally defined as the study of the laws of thought or correct reasoning, [5] and is usually understood in terms of inferences or arguments. Reasoning is the activity of drawing inferences. Arguments are the outward expression of inferences. [6] An argument is a set of premises together with a conclusion.

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