Titlebook: Logic: a Brief Course; Daniele Mundici Textbook 2012 Springer Milan 2012

fallible

Silent-Ischemia

Fundamental Logical NotionsFollowing the convention of the previous chapter, we use capital letters to denote variables. We need infinitely many variables, but by analogy with the keyboard of our computer we want to maintain our symbol apparatus, called the alphabet, finite. Therefore we represent officially the variables as ..

斜谷

Odyssey

Robinson’s Completeness TheoremAs we have seen, after a number of steps .. not exceeding the number of variables in .., DPP terminates producing as output a set .. of clauses without variables. .. can have only one of two possible forms: .. = □ or .. = ø

蒸发

Fast Classes for DPPIn some cases DPP proceeds fast, also with sets . of clauses having thousands of variables, whereas other procedures (e.g., the “truth table method”, in which one tries all assignments) would take geological time to decide whether . is satisfiable and to find an assignment if any.

Engulf

Propositional Logic: SyntaxWe now study a language, known as (Boolean, or classical) .. While it is more extended than the language of clauses considered so far, as we will see, it is not more expressive. For this language it is still possible to define precisely the concepts of satisfiability, logical equivalence and logical consequence.

Ferritin

Propositional Logic: SemanticsHaving completed the syntactic definitions we now pass on to the semantic definitions.

vitrectomy

Normal FormsWe now list some logical equivalences. Their proofs follow immediately from the definitions of the previous chapter. To facilitate the reading, outer parentheses are omitted throughout:

Working-Memory

使残废

Gödel’s Completeness Theorem for the Logic of ClausesThis fundamental theorem shows the equivalence of two at first sight different properties of a set of clauses .: