Complete Sets of Connectives andComplete
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منابع مشابه
Simple characterization of functionally complete one-element sets of propositional connectives
A set of propositional connectives is said to be functionally complete if all propositional formulae can be expressed using only connectives from that set. In this paper we give sufficient and necessary conditions for a one-element set of propositional connectives to be functionally complete. These conditions provide a simple and elegant characterization of functionally complete one-element set...
متن کاملComplete Sets of Connectives for Generalized Łukasiewicz Logics
While ∧,∨,¬ form a complete set of connectives for classical propositional logic, this does not hold for Łukasiewicz’s three-valued propositional logic, nor its generalization to n-valued logic. We define a unary connective r so that ∧,∨,¬, r form a complete set of connectives for n-valued Łukasiewicz logic. We discuss generalizations of this to infinitary logics. If we allow infinite conjuncti...
متن کاملSet-Oriented Logical Connectives: Syntax and Semantics
Of the common commutative binary logical connectives, only and and ormay be used as operators that take arbitrary numbers of arguments with order and multiplicity being irrelevant, that is, as connectives that take sets of arguments. This is especially evident in the Common Logic Interchange Format, in which it is easy for operators to be given arbitrary numbers of arguments. The reason is that...
متن کاملPost's Functional Completeness Theorem
The paper provides a new proof, in a style accessible to modern logicians and teachers of elementary logic, of Post's Functional Completeness Theorem. Post's Theorem states the necessary and sufficient conditions for an arbitrary set of (2-valued) truth functional connectives to be expressively complete, that is, to be able to express every (2-valued) truth function or truth table. The theorem ...
متن کاملPost's Functional Completeness Theorem
The paper provides a new proof, in a style accessible to modern logicians and teachers of elementary logic, of Post's Functional Completeness Theorem. Post's Theorem states the necessary and sufficient conditions for an arbitrary set of (2-valued) truth functional connectives to be expressively complete, that is, to be able to express every (2-valued) truth function or truth table. The theorem ...
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تاریخ انتشار 1996