Rigorous Software Development by José Bacelar Almeida Maria João Frade Jorge Sousa Pinto & Simão Melo de Sousa

Author:José Bacelar Almeida, Maria João Frade, Jorge Sousa Pinto & Simão Melo de Sousa
Language: eng
Format: epub
Publisher: Springer London, London

A formulaφ is -valid (resp. -satisfiable) if every (resp. some)-structure validatesφ. denotes the fact thatφ is-valid. Other concepts regarding validity of first-order formulas are carried over to theories in the obvious way.

A first-order theory is said to be aconsistent theory if at least one-structure exists. A consistent theory can also be characterised as a theory such that, for every-sentenceψ,. is said to be acomplete theory if, for every-sentenceφ, either or. is said to be adecidable theory if there exists a decision procedure for checking-validity.

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