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Extra info for O'Donnell M.J.Introduction.Logic and logic programming languages
Sample text
I be a query system, and let D = hFD D be a proof system with FQ FD . 2). If P is complete, then semantic correctness implies provable correctness. Going back to the communication analysis of previous sections, let Ks be the speaker's implicit knowledge, let K0a be the auditor's initial implicit knowledge, and let T0a be the auditor's initial explicit knowledge. When the speaker utters a set of formulae Tu , consistent with her implicit knowledge, the auditor's implicit knowledge improves as before to K1a =1 K0a \0 Models(Tu), and the auditor's explicit knowledge improves to Ta = Ta Tu .
Let fail be a new formal symbol, and let the set of naive implicational computations with failure be CS 2 = CS 1 : : : cm faili : c0 : : : cm 2 Atg (the set of nite and in nite sequences of atomic formulae, possibly ending in the special object fail). '). The computation relation S 2 is de ned by rest-imp(a A) T S 2 hc0 : : :i if and only if 1. c0 = a 2. if ci 2 A, and there is a d 2 At such that (ci ) d) 2 T, then the sequence has an i + 1st element ci+1 , and (ci ) ci+1 ) 2 T fhc0 Introduction 49 3.
All sorts of nonsensical formal systems t the de nitions. Rather, the relationships of soundness and completeness provide us with conceptual tools for evaluating the behavior of a proof system, with respect to a semantic system that we have already accepted as appropriate. Logic is distinguished from other technical sciences, not by the formal de nition of the systems that it studies, but rather by the use of logical concepts to evaluate these systems. The distinction between logic programming and other forms of programming is similarly based on the approach to evaluating the systems, rather than the formal qualities of the systems.