Handbook of Logic in Artificial Intelligence and Logic by Gabbay D.M., Hogger C.J., Robinson J.A. (eds.)

By Gabbay D.M., Hogger C.J., Robinson J.A. (eds.)

Common sense is now widely known as one of many foundational disciplines of computing and has functions in nearly all facets of the topic, from software program engineering and to programming languages and synthetic intelligence. The instruction manual of good judgment in synthetic Intelligence and its spouse The guide of good judgment in computing device technological know-how have been created in accordance with the transforming into desire for an in-depth survey of those purposes. This instruction manual contains 5 volumes, every one an in-depth evaluation of 1 of the foremost themes during this quarter. the results of years of cooperative attempt by means of across the world popular researchers, it is going to be the traditional reference paintings in AI for years yet to come. quantity five specializes in common sense programming. The chapters, which in lots of circumstances are of monograph size and scope, emphasize attainable unifying subject matters.

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Extra info for Handbook of Logic in Artificial Intelligence and Logic Programming. Volume 5: Logic Programming

Sample text

The following proof system follows the conventional style of textbooks in logic. Proofs are sequences of formulae, each one either a hypothesis, a postulate, or a consequence of earlier formulae in the proof. 2. Let FSh be the set of formulae in SIC. The set of linear proofs in SIC is PSl = F+sh, the set of nonempty finite sequences of formulae. , Fm) -si F if and only if Fm = F and, for alii < m, one of the following cases holds: 1. F; € T 2. Fi = (a =>• a) for some atomic formula a € At 3. Ft = 6, and there exist j, k < i such that Fj = a and Fk = (a => b) for some atomic formulae a, 6 e At 4.

I] is the formula that results from substituting the term tj for every occurrence of the variable Xj in the term t, for each j, 1 < j

An answer to such a question is an implication of the form F1 => FO , where F1 is an acceptable formula. The conventional FOPC questions (what x 1 , . . , xi : F0) may be understood as a variant of the 'what implies FO' questions, where the acceptable formulae are precisely those of the form x1 = t1 ^ . . ^ xi = t2. The proposed new style of FOPC question may be seen as presenting a set of constraints expressed by FO, and requesting a normalized expression of constraints F1 such that every solution to the constraints expressed by F1 is also a solution to the constraints of F0.

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