• The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes...
    118 KB (11,444 words) - 15:51, 30 May 2025
  • those built up from propositional variables using Boolean operations. Instantiation is still possible within propositional calculus, but only by instantiating...
    75 KB (9,572 words) - 01:33, 11 June 2025
  • the following Hilbert-style calculus. This is similar to a way of axiomatizing classical propositional logic. In propositional logic, the inference rule...
    53 KB (8,022 words) - 07:50, 29 April 2025
  • Two key uses of formulas are in propositional logic and predicate logic. A key use of formulas is in propositional logic and predicate logic such as...
    18 KB (2,164 words) - 01:24, 20 March 2025
  • the much simpler rules of propositional calculus. In a typical argument, quantifiers are eliminated, then propositional calculus is applied to unquantified...
    54 KB (6,091 words) - 07:55, 2 June 2025
  • mathematical logic, the implicational propositional calculus is a version of classical propositional calculus that uses only one connective, called implication...
    21 KB (3,081 words) - 03:37, 22 April 2025
  • This distinguishes it from propositional logic, which does not use quantifiers or relations;: 161  in this sense, propositional logic is the foundation of...
    92 KB (12,939 words) - 02:10, 16 June 2025
  • in connection with the classical propositional logic and with the so-called protothetic or quantified propositional logic; in both cases the law of non-contradiction...
    82 KB (11,576 words) - 03:49, 9 June 2025
  • concepts. In relation to the mind, propositions are discussed primarily as they fit into propositional attitudes. Propositional attitudes are simply attitudes...
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  • propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula...
    139 KB (11,131 words) - 00:07, 24 March 2025
  • false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics...
    4 KB (445 words) - 04:10, 4 October 2024
  • the modal μ-calculus (Lμ, Lμ, sometimes just μ-calculus, although this can have a more general meaning) is an extension of propositional modal logic (with...
    12 KB (1,816 words) - 21:25, 20 August 2024
  • Plankalkül (redirect from Plan Calculus)
    1938, Zuse discovered that the calculus he had independently devised already existed and was known as propositional calculus.: 3  What Zuse had in mind,...
    30 KB (2,743 words) - 09:09, 25 May 2025
  • logic is called complete.[citation needed] The completeness of the propositional calculus was proved by Paul Bernays in 1918[citation needed] and Emil Post...
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  • Thumbnail for Associative property
    rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions...
    26 KB (3,486 words) - 15:11, 9 June 2025
  • W. M. "Propositional logic" (PDF). It describes (among others) a specific Hilbert-style proof system (that is restricted to propositional calculus)....
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  • Thumbnail for Logical connective
    be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective ∨ {\displaystyle \lor } can be used to...
    34 KB (3,164 words) - 19:28, 10 June 2025
  • which can be either true (1), or false (0). In a classical propositional calculus, each proposition will be assigned a truth value of either true or false...
    6 KB (681 words) - 18:02, 21 April 2025
  • Hilbert-style deductive systems for propositional logics. Classical propositional calculus is the standard propositional logic. Its intended semantics is...
    19 KB (3,906 words) - 03:30, 22 April 2025
  • the last 2000 years, with the propositional Stoic logic. The two were sometimes seen as irreconcilable. Leibniz's calculus ratiocinator can be seen as foreshadowing...
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  • In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for...
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  • Aristotelian syllogisms alone. Taking propositional logic as given, every formula in the monadic predicate calculus expresses something that can likewise...
    6 KB (698 words) - 23:03, 22 February 2025
  • Thumbnail for Material conditional
    Implicational propositional calculus Laws of Form Logical graph Logical equivalence Material implication (rule of inference) Peirce's law Propositional calculus Sole...
    27 KB (2,229 words) - 15:03, 10 June 2025
  • schemata and modus ponens, one can prove all tautologies of the propositional calculus. It can also be shown that no pair of these schemata is sufficient...
    34 KB (4,918 words) - 17:20, 17 May 2025
  • expression from premises Propositional calculus, specifies the rules of inference governing the logic of propositions Predicate calculus, specifies the rules...
    5 KB (671 words) - 05:49, 20 August 2024
  • function. The logical axioms of PRA are the: Tautologies of the propositional calculus; Usual axiomatization of equality as an equivalence relation. The...
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  • specified – see § Propositional inference rules (Suppes–Lemmon style). This section defines the formal syntax for a propositional logic language, contrasting...
    75 KB (7,770 words) - 09:00, 6 June 2025
  • simply the propositional calculus augmented by □, the rule N, and the axiom K. K is weak in that it fails to determine whether a proposition can be necessary...
    61 KB (8,679 words) - 01:32, 16 June 2025
  • co-NP complete. In the case of classical propositional logic, satisfiability is decidable for propositional formulae. In particular, satisfiability is...
    12 KB (1,500 words) - 23:20, 22 May 2025
  • Thumbnail for Logical conjunction
    disjunction Logical graph Negation Operation Peano–Russell notation Propositional calculus "2.2: Conjunctions and Disjunctions". Mathematics LibreTexts. 2019-08-13...
    18 KB (1,465 words) - 05:16, 22 February 2025