By Alexander Bochman

ISBN-10: 3642075169

ISBN-13: 9783642075162

ISBN-10: 3662045605

ISBN-13: 9783662045602

The major topic and goal of this publication are logical foundations of non monotonic reasoning. This bears a presumption that there's any such factor as a normal thought of non monotonic reasoning, rather than a host of structures for the sort of reasoning latest within the literature. It additionally presumes that this sort of reasoning should be analyzed through logical instruments (broadly understood), simply as the other form of reasoning. with a purpose to in attaining our objective, we are going to offer a typical logical foundation and semantic illustration within which other kinds of non monotonic reasoning may be interpreted and studied. The prompt framework will subsume ba sic different types of nonmonotonic inference, together with not just the standard skeptical one, but in addition a number of different types of credulous (brave) and defeasible reasoning, in addition to a few new forms corresponding to contraction inference relatives that specific relative independence of items of information. furthermore, an analogous framework will function a foundation for a common concept 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 optimistic 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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**Extra info for A Logical Theory of Nonmonotonic Inference and Belief Change**

**Example text**

If u is saturatable with respect to -,A, either A V B or A V -,B belongs to u, and therefore either a, A V B ¥ A or a, A V -,B ¥ A. Hence Weak Factoring holds. ,A V -,B should belong to u by Weak Factoring, and hence Cl( u U {A}) is a world. D 28 2. Consequence Relations The next result shows that Weak Factoring is equivalent to a certain weak form of Disjunction in the Antecedent. 5. A supraclassical consequence relation is semi-classical iff it satisfies the following rule: Weak Disjunction If a, AV B f- A and a, AVe f- A, then a, A V BVe f- A.

A set of propositions ,1 will be called A-closed, if, for any A, BELl, AAB also belongs to ,1. 1. If- is base generated iff it is generated by a A-closed set of propositions. Propositions from a base of a consequence relation can be freely combined in order to produce new theories. In particular, it is easy to show that Th(Ll) is the greatest theory of such a consequence relation. 1. Any base-generated consequence relation is determinate. Proof. If AW, there must exist a subset b of the base such that A E Th(b).

Let T be a union-closed right-compact set of theories of If-, and U and v are two arbitrary theories of If-. Since T is right-compact, U = UU and v = UV, for some subsets U and V of T. Now consider the set W of theories CI( Ui UVj), for all Ui E U and Vj E V. Since T is union-closed, W is included in T, and hence all theories are theories of If-. Moreover, the set W is directed. Indeed, any two theories CI(Ul,Vl) and CI(u2, V2) from Ware included into the theory CI(CI(Ul, U2), CI(Vl, V2)), which also belongs to W.

### A Logical Theory of Nonmonotonic Inference and Belief Change by Alexander Bochman

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