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PDL blends the ideas behind propositional logic and dynamic logic by adding actions while omitting data; hence the terms of PDL are actions and propositions. The TV example above is expressed in PDL whereas the next example involving := + is in first-order dynamic logic. PDL is to (first-order) dynamic logic as propositional logic is to first ...
2.2 Example. 3 Proof. 4 Relation to functions. 5 ... Import-export is a name given to the statement as a theorem or truth-functional tautology of propositional logic
In propositional logic, modus ponens (/ ˈ m oʊ d ə s ˈ p oʊ n ɛ n z /; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3]
Going further, for every proof in the logic, there was a matching function (term) in the programming language. One of Curry's examples was the correspondence between simply typed lambda calculus and intuitionistic logic. [2] Predicate logic is an extension of propositional logic, adding quantifiers.
Together with the normal forms in propositional logic (e.g. disjunctive normal form or conjunctive normal form), it provides a canonical normal form useful in automated theorem proving. Every formula in classical logic is logically equivalent to a formula in prenex normal form.
It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic. [ b ] [ 6 ] [ 7 ] [ 8 ] Sometimes, it is called first-order propositional logic [ 9 ] to contrast it with System F , but it should not be confused with first-order logic .
Classical propositional calculus is the standard propositional logic. Its intended semantics is bivalent and its main property is that it is strongly complete, otherwise said that whenever a formula semantically follows from a set of premises, it also follows from that set syntactically. Many different equivalent complete axiom systems have ...
Other examples of atoms include x, blue, 'Taco', and 'some atom'. Numbers can be floats or integers. Many Prolog implementations also provide unbounded integers and rational numbers. Variables are denoted by a string consisting of letters, numbers and underscore characters, and beginning with an upper-case letter or underscore. Variables ...