The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes...
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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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Boolean algebra (section Propositional logic)
those built up from propositional variables using Boolean operations. Instantiation is still possible within propositional calculus, but only by instantiating...
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Intuitionistic logic (redirect from Intuitionistic propositional calculus)
the following Hilbert-style calculus. This is similar to a way of axiomatizing classical propositional logic. In propositional logic, the inference rule...
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mathematical logic, the implicational propositional calculus is a version of classical propositional calculus that uses only one connective, called implication...
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Well-formed formula (section Propositional calculus)
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...
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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...
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the much simpler rules of propositional calculus. In a typical argument, quantifiers are eliminated, then propositional calculus is applied to unquantified...
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First-order logic (redirect from First-order predicate calculus)
This distinguishes it from propositional logic, which does not use quantifiers or relations;: 161 in this sense, propositional logic is the foundation of...
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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...
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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...
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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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false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics...
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Associative property (section Propositional logic)
rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions...
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expression from premises Propositional calculus, specifies the rules of inference governing the logic of propositions Predicate calculus, specifies the rules...
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Hilbert system (redirect from Hilbert calculus)
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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List of axiomatic systems in logic (redirect from Positive propositional calculus)
Hilbert-style deductive systems for propositional logics. Classical propositional calculus is the standard propositional logic. Its intended semantics is...
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Rule of inference (section Propositional logic)
Propositional logic is not concerned with the concrete meaning of propositions other than their truth values. Key rules of inference in propositional...
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Logical connective (redirect from Propositional operator)
be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective ∨ {\displaystyle \lor } can be used to...
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co-NP complete. In the case of classical propositional logic, satisfiability is decidable for propositional formulae. In particular, satisfiability is...
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communicative. Thus Mentalese is best expressed through predicate and propositional calculus.[citation needed] Made up of discrete symbols; each symbol has a...
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Axiom (section Propositional logic)
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...
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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...
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Implicational propositional calculus Laws of Form Logical graph Logical equivalence Material implication (rule of inference) Peirce's law Propositional calculus Sole...
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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,...
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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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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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Natural deduction (redirect from Natural deduction calculus)
specified – see § Propositional inference rules (Suppes–Lemmon style). This section defines the formal syntax for a propositional logic language, contrasting...
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the basis of propositional calculus Independently, in the 1870's, Charles Sanders Peirce and Gottlob Frege extended propositional calculus by introducing...
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Modal logic (redirect from Impossible proposition)
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...
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