By Alexander Bochman
The major topic and aim of this booklet are logical foundations of non monotonic reasoning. This bears a presumption that there's any such factor as a basic concept of non monotonic reasoning, instead of a host of platforms for the sort of reasoning latest within the literature. It additionally presumes that this sort of reasoning will be analyzed via logical instruments (broadly understood), simply as the other form of reasoning. with the intention to in attaining our aim, we are going to offer a typical logical foundation and semantic illustration within which other forms of non monotonic reasoning will be interpreted and studied. The steered framework will subsume ba sic varieties of nonmonotonic inference, together with not just the standard skeptical one, but in addition a number of sorts of credulous (brave) and defeasible reasoning, in addition to a few new types reminiscent of contraction inference family that categorical relative independence of items of information. additionally, a similar framework will function a foundation for a normal concept of trust swap which, between different issues, will let us unify the most ways to trust swap current within the literature, in addition to to supply a confident view of the semantic illustration used. This booklet is a monograph instead of a textbook, with all its merits (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
2. A consequence relation If- is base-generated if and only if the set of its base propositions forms a base of If- (relative to Th1f-). In other words, the set of all base propositions of a base-generated consequence relation can be seen as its canonical base. 1 Union-closure and strong base-generation In this section we will give an important alternative characterization of basegenerated consequence relations. A set T of deductively closed theories will be called union-closed if, for any theories Ul, U2 from T, CI( Ul UU2) also belongs to T.
Clearly, this theory cannot be prime. We will show, however, that u is a minimal theory containing p. Assume first that there exists a finite set C such that u If- c, though c is disjoint from u. Then the conjunctive normal form of any C E c must contain a disjunction Cd of literals without positive occurrences of p's. Let Cd be a 34 2. Consequence Relations set of such disjunctions, for all C E c. Then we still have that Cd is disjoint from u and u If- Cd. Moreover, by compactness, P,PI, ... ,Pn If- Cd, for some natural n.
In this way we will try to avoid both over-simplification and excessive abstraction of our models. Throughout this chapter we will also establish links and relations between our semantic rep·· resentation and other models of nonmonotonic reasoning and belief change suggested in the literature. 1 General epistemic states As we said in the introduction, humans do not just collect data and make logical conclusions, they try to explain what they see and predict consequences of their potential actions, even if not all aspects and facts about the situation are known.
A Logical Theory of Nonmonotonic Inference and Belief Change by Alexander Bochman