By Alexander Bochman

ISBN-10: 3642075169

ISBN-13: 9783642075162

ISBN-10: 3662045605

ISBN-13: 9783662045602

The major topic and aim of this booklet are logical foundations of non monotonic reasoning. This bears a presumption that there's the sort of factor as a common thought of non monotonic reasoning, instead of a host of platforms for this sort of reasoning current within the literature. It additionally presumes that this type of reasoning will be analyzed through logical instruments (broadly understood), simply as the other form of reasoning. for you to in attaining our objective, we are going to supply a standard logical foundation and semantic illustration within which other forms of non monotonic reasoning may be interpreted and studied. The prompt framework will subsume ba sic types 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 reminiscent of contraction inference kin that categorical relative independence of items of information. moreover, 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 swap latest within the literature, in addition to to supply a optimistic view of the semantic illustration used. This e-book 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**

**Sample text**

2. If a consequence relation If- is strongly grounded, then any theory u of If- is equal to Thlfo(u n Plfo). Proof. If If- is strongly grounded, then each its theory u is a union of all Th(A), where A E P lfo n u, and hence u coincides with Thlfo(u n P lfo ). 0 Clearly, any strongly grounded consequence relation will be grounded, though not vice versa. The following example illustrates this. 1. 1 be a set of all propositions En = PI\Pll\·· ·I\Pn 1\ qn, for all natural n. 1 with respect to the classical entailment C1.

If B --t c (since Th1f-(A) is a theory). Therefore there must exist Bl E Ll'" such that A E Th(Bd and B --t c <;;; Th(Bd. The later condition implies that c is disjoint from Th(B 1\ Bd. In addition, Th(B 1\ Bd includes 2 This was the case considered, in effect, in [Boc99b]. 38 2. Consequence Relations both A and a. But B /\ Bl belongs to Ll/\, and hence a, A W c. Therefore, A is a base proposition of If-. 0 As was shown earlier, any base-generated consequence relation is grounded, that is, generated by its prime theories.

A supraclassical Scott consequence relation will be called • finite if it is a least consequence relation containing some finite set of sequents . • finitary if it is generated by a finite set of prime theories. 3. Any finitary consequence relation is strongly grounded. However, a finite consequence relation has, in general, an infinite number of theories. 4. Any finite consequence relation is strongly grounded. Proof. Assume that If- is generated by a finite set of sequents {ai If- cd, and let h denote a (finite) set of all propositions occurring in their conclusions, that is, h = Ui(Ci).

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

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