Logic for Computer Science and Artificial Intelligence
Ricardo Caferra
Language: English
Pages: 544
ISBN: 1848213018
Format: PDF / Kindle (mobi) / ePub
Logic and its components (propositional, first-order, non-classical) play a key role in Computer Science and Artificial Intelligence. While a large amount of information exists scattered throughout various media (books, journal articles, webpages, etc.), the diffuse nature of these sources is problematic and logic as a topic benefits from a unified approach. Logic for Computer Science and Artificial Intelligence utilizes this format, surveying the tableaux, resolution, Davis and Putnam methods, logic programming, as well as for example unification and subsumption. For non-classical logics, the translation method is detailed.
Logic for Computer Science and Artificial Intelligence is the classroom-tested result of several years of teaching at Grenoble INP (Ensimag). It is conceived to allow self-instruction for a beginner with basic knowledge in Mathematics and Computer Science, but is also highly suitable for use in traditional courses. The reader is guided by clearly motivated concepts, introductions, historical remarks, side notes concerning connections with other disciplines, and numerous exercises, complete with detailed solutions, The title provides the reader with the tools needed to arrive naturally at practical implementations of the concepts and techniques discussed, allowing for the design of algorithms to solve problems.
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And 9.28. D EFINITION 2.3.– A language is extensional iff any sentence in this language has the same truth value when one of its components is replaced by another component with the same truth value. A connective is extensional if the truth value of composed propositions only depends on the truth value of their components. Only using an extensional approach leads to a loss in the expressive power of the language. E XAMPLE 2.6.– (a non-extensional language (R. Carnap)). 1) It is raining F % it is.
P(L) × P(L) is a consequence relation in L11 iff it satisfies the following conditions: A, B ∈ L. A, B, A , B , C ⊆ L A, B: A ∪ B A, B: A ∪ {B} (R) A A if A = ∅ (reflexivity) (M ) if A B then A, A B, B (monotonicity) (T ) if A B, C and A, B C then A Thanks to properties (R), (M ) and (T ), partial order (see definition 3.23). C (transitivity) can be viewed as a generalization of a It is fairly simple to show that a consequence relation à la Scott is a consequence relation à la Tarski, and.
If we do not succeed, then we were Propositional Logic 55 unable to refute the reasoning, because we were unable to evaluate the premises to true and the conclusion to false (as we tried to evaluate the negation of the conclusion to true). Hence, the reasoning is correct. However, if we succeed, then we will have produced a counter example that proves the reasoning is not correct. We also noticed that it is not always necessary to construct an entire truth table to evaluate a formula to true.
Maintain that mathematical studies have an important empirical component (and therefore inherit its methods: reproducibility of the experiments, etc.12). It is interesting to compare the theses given above with the thoughts that inspired a mathematician (C.W.H. Lam) in his own work, as he obtained new results (in 1977) using a computer. He begins his article by explaining his work, using the title of an article that had appeared in a general magazine: Is a math proof a proof if no one can check.
We can imagine, thinking of their formulas and theorems, that “nothing gets past them”. This characteristic is mirrored in the formalist school of thought, which insisted on the purely formal side of mathematics (i.e. an activity entirely controlled by the rules of the game), and of which the great mathematician D. Hilbert was one of the principal advocates. In what is called “Hilbert’s program”, Hilbert, who wanted to obtain sound foundations for mathematics, stated the problem of finding a.