By Alexander Bochman

ISBN-10: 3642075169

ISBN-13: 9783642075162

ISBN-10: 3662045605

ISBN-13: 9783662045602

The major topic and target of this booklet are logical foundations of non monotonic reasoning. This bears a presumption that there's any such factor as a normal conception of non monotonic reasoning, instead of a number of platforms for one of these reasoning present within the literature. It additionally presumes that this type of reasoning may be analyzed through logical instruments (broadly understood), simply as the other form of reasoning. so that it will in attaining our target, we'll supply a typical logical foundation and semantic illustration during which other forms of non monotonic reasoning should be interpreted and studied. The instructed framework will subsume ba sic varieties of nonmonotonic inference, together with not just the standard skeptical one, but additionally a number of kinds of credulous (brave) and defeasible reasoning, in addition to a few new forms reminiscent of contraction inference family members that categorical relative independence of items of information. moreover, an identical framework will function a foundation for a basic conception of trust switch which, between different issues, will let us unify the most methods to trust switch current within the literature, in addition to to supply a optimistic view of the semantic illustration used. This publication 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 resources for A Logical Theory of Nonmonotonic Inference and Belief Change**

**Example text**

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). Let u be a minimal theory containing a proposition A. We will show that u = CI(A 1\ Hu), where Hu denotes a conjunction of all propositions from h belonging to u. To this end, it is sufficient to show that CI(A 1\ Hu) is a theory of If- (since it is included in u).

In the other direction, assume that u is a theory of hf- which is distinct from the set of all propositions, that is A ~ u, for some A. Then u W A, and hence there is a theory v of If- such that u ~ v and A ~ v. Consequently, any theory of hf- coincides with an intersection of all theories of If- that include u. 0 The following lemma will be used in the sequel. 2. A theory u of a Scott consequence relation If- is a least theory containing a set of propositions v if and only if u = Cnlf- (v). Proof.

A base-generated consequence relation If- is strongly grounded iff the set of theories of If- coincides with T(f'. Proof. A base-generated consequence relation is strongly grounded iff any of its theories is a union of prime theories. Consequently any theory u will coincide with Th(u n Lllf-), and hence all theories of If- will be deductive closures of base propositions. 3. A consequence relation is base-generated and strongly grounded iff the set of theories T(f' is compact. The next result shows that, for strongly grounded consequence relations, base-generation is equivalent to union closure.

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

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