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

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 kind of factor as a basic concept of non monotonic reasoning, in place of a host of structures for this type of reasoning current within the literature. It additionally presumes that this type of reasoning could be analyzed through logical instruments (broadly understood), simply as the other type of reasoning. with a view to in attaining our target, we are going to offer a standard logical foundation and semantic illustration within which other kinds of non monotonic reasoning might be interpreted and studied. The urged framework will subsume ba­ sic sorts of nonmonotonic inference, together with not just the standard skeptical one, but in addition numerous sorts of credulous (brave) and defeasible reasoning, in addition to a few new varieties equivalent to contraction inference family members that specific relative independence of items of knowledge. moreover, a similar framework will function a foundation for a common conception of trust swap which, between different issues, will let us unify the most techniques to trust swap present 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 resources for A Logical Theory of Nonmonotonic Inference and Belief Change

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Proof. The inclusion of left into right is immediate. Let If- be a Scott consequence relation and a W b, for some a and b. Then there exists a theory u of If- that includes a and is disjoint from b. 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.

Show that if u is a maximal theory of r that does not contain a proposition A, then Cl(u, A) is also a theory of r. 1. 1 such that A E Th~(D). 1, for any A. 3. Epistemic States Introduction Semantic interpretation constitutes one of the main components of a viable reasoning system, monotonic or not. A formal inference engine, though important in its own right, can be effectively used for representing and solving commonsense reasoning tasks only if its basic inference steps possess a clear meaning allowing us to discern them from a description of a situation at hand.

0 26 2. Consequence Relations Supraclassicality allows for replacement of classically equivalent formulas in premises and conclusions of the rules. In addition, it allows to replace sets of premises by their classical conjunctions: a f- A will be equivalent to 1\ a f- A. Accordingly, supraclassical Tarski consequence relations can be reduced to certain binary relations among classical propositions. This fact will play an important role in Chapter 5. It should be noted, however, that provable equivalence with respect to a supraclassical consequence relation does not imply that the corresponding formulas are interchangeable in all contexts.

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