By Alexander Bochman
The major topic and target of this ebook are logical foundations of non monotonic reasoning. This bears a presumption that there's this type of factor as a basic thought of non monotonic reasoning, in place of a number of platforms for one of these reasoning latest within the literature. It additionally presumes that this type of reasoning will be analyzed via logical instruments (broadly understood), simply as the other form of reasoning. for you to in achieving our aim, we'll offer a typical logical foundation and semantic illustration during which other kinds of non monotonic reasoning will be interpreted and studied. The recommended 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 forms resembling contraction inference kin that specific relative independence of items of knowledge. furthermore, an identical framework will function a foundation for a common concept 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 publication 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 resources for A Logical Theory of Nonmonotonic Inference and Belief Change
3 Semi-classical consequence relations We will describe below a very special kind of Tarski consequence relation that will playa central role in our analysis of nonmonotonic inference. A supraclassical Tarski consequence relation will be called semi-classical if it is closed with respect to the following weak rule of reasoning by cases: Weak Factoring If a, A V B I- A and a, A V -,B I- A, then a I- A. Clearly, any classical consequence relation is semi-classical, though not vice versa. A semantic characterization of such consequence relations can be given in terms of so-called saturatable theories introduced in [Lev91].
1 will be prime in If-. 1 A . 1 A by right compactness. Assume that If- satisfies the above two conditions, and let u be a minimal theory of If- containing some proposition A. 1 A . But D is a prime proposition, and hence Th1f-(D) will be a theory of If- that contains A and is included in u. Due to minimality of u, we have u = Thlf-(D). 1. 5 Base-generated consequence relations In this section we will give a characterization of Scott consequence relations that are generated by subsets of a certain set of propositions called its base.
Epistemic States epistemic states. The latter guide our decisions as to what to believe and what not to believe when, for example, the situation changes. Studies in nonmonotonic reasoning have suggested a new general approach to such 'belief support' systems according to which our beliefs are formed with the help of defaults, or expectations, that we are willing to accept in the absence of evidence to the contrary. In many situations, however, different defaults may conflict both with one another and with known facts, and this gives us several admissible subsets of defaults forming a basis for different plausible sets of beliefs we can hold in such situations.