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

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By Alexander Bochman

The major topic and goal of this booklet are logical foundations of non­ monotonic reasoning. This bears a presumption that there's the sort of factor as a common concept of non monotonic reasoning, rather than a number of platforms for this kind of reasoning latest 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. with the intention to in achieving our objective, we are going to supply a standard logical foundation and semantic illustration within which other kinds of non monotonic reasoning may be interpreted and studied. The instructed framework will subsume ba­ sic types of nonmonotonic inference, together with not just the standard skeptical one, but additionally a variety of types of credulous (brave) and defeasible reasoning, in addition to a few new forms comparable to contraction inference kin that categorical relative independence of items of information. additionally, a similar framework will function a foundation for a basic idea of trust switch which, between different issues, will let us unify the most ways to trust switch present 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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The most topic and aim of this e-book are logical foundations of non­ monotonic reasoning. This bears a presumption that there's one of these factor as a common concept of non monotonic reasoning, rather than a number of platforms for one of these reasoning latest within the literature. It additionally presumes that this type of reasoning will be analyzed by means of logical instruments (broadly understood), simply as the other form of reasoning.

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Extra info for A Logical Theory of Nonmonotonic Inference and Belief Change

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If a ¥ A, there must exist a maximal theory u that is consistent with -,A and includes a. 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.

It is important to note that this structure implicitly reflects dependence relations among potential beliefs. The latter, even if logically consistent, can be based on incompatible defaults and expectations, and hence cannot always be held simultaneously. Accordingly, admissible belief sets are not homogeneous; not all deletions or additions to them constitute justifiable belief sets, but only those that are supported by some admissible sets of defaults. In other words, potential beliefs are correlated, and some of them serve as reasons, or justification, for others.

In particular, imposing some finiteness restrictions will enforce strong generation. 5. 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.

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