By Alexander Bochman
The major topic and target of this ebook are logical foundations of non monotonic reasoning. This bears a presumption that there's this kind of factor as a normal thought of non monotonic reasoning, in place of a host of platforms for any such reasoning present within the literature. It additionally presumes that this type of reasoning will be analyzed via logical instruments (broadly understood), simply as the other type of reasoning. so one can in attaining our aim, we'll offer a typical logical foundation and semantic illustration during which other forms of non monotonic reasoning might be interpreted and studied. The urged framework will subsume ba sic sorts of nonmonotonic inference, together with not just the standard skeptical one, but additionally quite a few sorts of credulous (brave) and defeasible reasoning, in addition to a few new varieties comparable to contraction inference relatives that specific relative independence of items of knowledge. moreover, an identical framework will function a foundation for a normal conception of trust swap which, between different issues, will let us unify the most ways to trust switch latest within the literature, in addition to to supply a confident view of the semantic illustration used. This booklet is a monograph instead of a textbook, with all its merits (mainly for the writer) and shortcomings (for the reader).
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Additional info for A Logical Theory of Nonmonotonic Inference and Belief Change
0 As a consequence of the above result, we obtain that any right-compact set of theories of a supraclassical consequence relation will also be a generating set of theories. 1. If a set of theories T is right-compact in a supraclassical consequence relation, then the latter is generated by T. Proof. Follows from the fact that T is right-compact if and only if it includes 0 the set of small theories. A supraclassical Scott consequence relation will be called classically consistent if the set of all propositions is not its theory.
4 Grounded Scott consequence relations In this section we will consider supraclassical Scott consequence relations that are generated, in a certain sense, by sets of propositions. The construction below describes one of the important ways of building Scott consequence relations. Though it could be given in a more general setting, the level of generality chosen will be sufficient for our purposes. :1 a set propositions. :1}. :1 (relative to Th). It turns out that there exists a purely internal characterization of classically generated consequence relations.
2. A supraclassical consequence relation is strongly grounded iff it is strongly generated by some set of propositions. The following result connects the notion of strong groundedness with the general notion of right compactness. 3. A supra classical consequence relation is strongly grounded if and only if the set of its prime theories is right-compact. Proof. Follows from the fact that a set of theories is right-compact iff it includes the set of small theories. 1. A consequence relation is strongly grounded if and only if all its theories are unions of prime theories.