Craig interpolation for networks of sentences
نویسندگان
چکیده
منابع مشابه
Craig interpolation for networks of sentences
The Craig Interpolation Theorem can be viewed as saying that in first order logic, two agents who can only communicate in their common language can cooperate in building proofs. We obtain generalizations of the Craig Interpolation Theorem for finite sets of agents with the following properties. (1) The agents are vertices of a directed graph. (2) The agents have knowledge bases with overlapping...
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It seems to be an open question whether Propositional Dynamic Logic (PDL) has Craig Interpolation. In fact, it even seems to be an open question if this is an open question: Multiple proofs have been claimed to be found but all of them also have been claimed to be wrong, both more or less publicly. This report tries to clarify the situation by discussing the proof by Daniel Leivant [11] from 19...
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1 Background and Introduction Let 27 and H be two inconsistent first order theories. Then by Craig's Interpolation Theorem, there is a sentence 8, called a Craig interpolant, such that 8 is t rue in 27 and false in H and every nonlogical symbol occurring in 8 occurs in bo th 27 and H. Craig interpolants can be used to solve the problem of learning a first order concept by letting 27 and H be th...
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Generalizations of Craig interpolation are investigated for equational logic. Our approach is to do as much as possible at a categorical level, before drawing out the concrete implications.
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2012
ISSN: 0168-0072
DOI: 10.1016/j.apal.2012.03.001