By Alexander Bochman

The major topic and target of this publication are logical foundations of non­ monotonic reasoning. This bears a presumption that there's this type of factor as a basic concept of non monotonic reasoning, in place of a number of platforms for one of these reasoning current within the literature. It additionally presumes that this type of reasoning should be analyzed through logical instruments (broadly understood), simply as the other type of reasoning. to be able to in attaining our aim, we'll supply a typical logical foundation and semantic illustration during which other forms of non monotonic reasoning might be interpreted and studied. The prompt framework will subsume ba­ sic varieties of nonmonotonic inference, together with not just the standard skeptical one, but additionally quite a few types of credulous (brave) and defeasible reasoning, in addition to a few new types similar to contraction inference family members that categorical relative independence of items of knowledge. moreover, an analogous framework will function a foundation for a normal conception of trust swap which, between different issues, will let us unify the most techniques to trust switch latest within the literature, in addition to to supply a positive view of the semantic illustration used. This booklet is a monograph instead of a textbook, with all its benefits (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

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A supra classical Tarski consequence relation is union-closed if and only if it satisfies Cn(A /\ B) = CI(Cn(A), Cn(B)) Proof. The direction from left to right is immediate. Let u and v be two theories of f- and u, v f- A. then there must exist B E u and C E v such that B, C f- A. By the above condition, this implies A E Cl(Cn(B), Cn(C)), and hence there must exist B1 E Cn(B) and C1 E Cn( C) such that C1, B1 fA. But B1 belongs to u, while C1 belongs to v, and therefore u, v f- A. Consequently, f- is union-closed.

Linear Scott consequence relations do not satisfy, however, the first characteristic property of singular consequence relations, since the set of all propositions does not always form a theory. Still, such consequence relations can be studied in the framework of Tarski consequence relations, with the only reservation that Scott consequence relations are capable of distinguishing between cases where the set of all propositions is a theory and those where it is not. 3 Supraclassicality Now we will consider consequence relations in languages containing the usual classical connectives {V, 1\, --', -+}.

More exactly, there is a one-to-one correspondence between Tarski consequence relations and singular Scott consequence relations satisfying the following condition: (Singularity) If a If- b, then a If- B, for some B E b. A characteristic 'semantic' feature of a singular Scott consequence relation is that intersection of any set of its theories is also a theory of a consequence relation. 3. A Scott consequence relation If- is singular if and only if 1. The set of all propositions of the language is a theory of If-; 2.

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