By Alexander Bochman

ISBN-10: 3642075169

ISBN-13: 9783642075162

ISBN-10: 3662045605

ISBN-13: 9783662045602

The major topic and target of this ebook are logical foundations of non monotonic reasoning. This bears a presumption that there's any such factor as a common idea of non monotonic reasoning, instead of a number of platforms for the sort of reasoning latest within the literature. It additionally presumes that this type of reasoning may be analyzed through logical instruments (broadly understood), simply as the other type of reasoning. for you to in achieving our aim, we are going to supply a standard logical foundation and semantic illustration during which other forms of non monotonic reasoning could be interpreted and studied. The instructed framework will subsume ba sic sorts of nonmonotonic inference, together with not just the standard skeptical one, but in addition a number of types of credulous (brave) and defeasible reasoning, in addition to a few new types resembling contraction inference family that specific relative independence of items of information. furthermore, an analogous framework will function a foundation for a common concept of trust switch which, between different issues, will let us unify the most methods to trust swap present within the literature, in addition to to supply a optimistic view of the semantic illustration used. This ebook is a monograph instead of a textbook, with all its benefits (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**

Now, since the union of any chain of theories from If- is also a theory of If-, u is included in some maximal chain of theories Ti (by Zorn's lemma). Let If-I be a Scott consequence relation determined by Ti. Clearly, If-I is a linear consequence relation that extends If-. In addition, u is a theory of If-I, and hence a Wi b. Thus, If- coincides with the 0 intersection of linear consequence relations that extend it. As will be shown in what follows, a similar 'linear decomposition' will also hold for quite rich partially ordered structures of epistemic states.

A theory ofl'r will be called prime, ifu = Th1f-(A), for some proposition A. 32 2. Consequence Relations • A proposition A will be called prime in II-, if Thll- (A) is a theory of II-. It is easy to show that if A is a prime proposition, then Thlf- (A) is a least theory of II- containing A. Consequently, any prime theory will be small. Note also that all prime propositions 'generating' a given prime theory are equivalent modulo Th1f-. The next lemma gives an alternative description of prime propositions.

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. Consequently, the union UW is also a theory of If-. But it can be easily checked that this theory coincides with CI(u, v). So, CI(u,v) is also a theory of If-, and hence If- is union-closed. 0 The next result connects the notion of union-closure with that of basegeneration. 4. If a set of theories of a grounded consequence relation If- is union-closed, then II- is base-generated.

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

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