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Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
, 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
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Cited by 538 (13 self)
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Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both prooftheoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams in [2]. The pr...
Semantic Belief Change
, 1999
"... The ability to change one's beliefs in a rational manner is one of many facets of the abilities of an intelligent agent. Central to any investigation of belief change is the notion of an epistemic state. This dissertation is mainly concerned with three issues involving epistemic states: 1. How shou ..."
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Cited by 3 (2 self)
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The ability to change one's beliefs in a rational manner is one of many facets of the abilities of an intelligent agent. Central to any investigation of belief change is the notion of an epistemic state. This dissertation is mainly concerned with three issues involving epistemic states: 1. How should an epistemic state be represented? With regard to the first question, note that there are many different methods for constructing belief change operations. We argue that semantic constructions involving ordered pairs, each consisting of a set of beliefs and an ordering on the set of "possible worlds" (or equivalently, on the set of basic independent bits of information) are, in an important sense, more fundamental.
Logical Constants Across Varying Types
 Notre Dame Journal of Formal Logic
, 1989
"... Abstract We investigate the notion of "logicality " for arbitrary categories of linguistic expression, viewed as a phenomenon which they can all possess to a greater or lesser degree. Various semantic aspects of logicality are analyzed in technical detail: in particular, invariance for per ..."
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Cited by 1 (0 self)
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Abstract We investigate the notion of "logicality " for arbitrary categories of linguistic expression, viewed as a phenomenon which they can all possess to a greater or lesser degree. Various semantic aspects of logicality are analyzed in technical detail: in particular, invariance for permutations of individual objects, and respect for Boolean structure. Moreover, we show how such properties are systematically related across different categories, using the apparatus of the typed lambda calculus. 315 / The range of logicality Philosophical discussions of the nature of logical constants often concentrate on the connectives and quantifiers of standard predicate logic, trying to find out what makes them so special. In this paper, we take logicality in a much broader sense, including special predicates among individuals such as identity ("be") or higher operations on predicates such as reflexivization ("self"). One convenient setting for achieving the desired generality is that of a standard Type Theory, having primitive types e for entities and t for truth values, while forming functional compounds (a,b) out of already available types a and b. Thus, e.g., a oneplace predicate of individuals has type (e,t) (assigning truth values to individual entities), whereas a twoplace predicate has type (e, (e, t)). Higher types occur, among others, with quantifiers, when regarded in the Fregean style as denoting properties of properties: ((e,t)9t). For later reference, here are some types, with categories of expression taking a corresponding denotation: e entities proper names / truth values sentences (t,t) unary connectives sentence operators