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Circumscribing with sets
 Artificial Intelligence
, 1987
"... Abstract: Sets can play an important role in circumscription’s ability to deal in a general way with certain aspects of commonsense reasoning. Aresult of Kueker indicates that sentences that intuitively one would want circumscription to prove, are nonetheless not so provable in a formal setting devo ..."
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Cited by 10 (5 self)
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Abstract: Sets can play an important role in circumscription’s ability to deal in a general way with certain aspects of commonsense reasoning. Aresult of Kueker indicates that sentences that intuitively one would want circumscription to prove, are nonetheless not so provable in a formal setting devoid of sets. Furthermore, when sets are introduced, firstorder circumscription handles these cases very easily, obviating the need for secondorder circumscription. The Aussonderungs axiom of ZF set theory plays an intuitive role in this shift back to a firstorder language. descriptors: commonsense, circumscription, sets I.
Defaults Denied
 In preparation
, 1994
"... We take a tour of various themes in default reasoning, examining new ideas as well as those of Brachman, Delgrande, Poole, and Schlechta. An underlying issue is that of stating that a potential default principle is not appropriate. We see this arise most dramatically as a problem in an attempt to fo ..."
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Cited by 2 (2 self)
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We take a tour of various themes in default reasoning, examining new ideas as well as those of Brachman, Delgrande, Poole, and Schlechta. An underlying issue is that of stating that a potential default principle is not appropriate. We see this arise most dramatically as a problem in an attempt to formalize what are often loosely called "prototypes", although it also arises in other formal approaches to default reasoning. Some formalisms in the literature provide solutions but not without costs. We propose a formalism that appears to avoid these costs; it can be seen as a step toward a populationbased settheoretic modification of these approaches, that may ultimately provide a closer tie to recent work on statistical (quantitative) foundations of (qualitative) defaults([1]). Our analysis in particular indicates the need to resolve a conflation between use and mention in many default formalisms. Our treatment proposes such a resolution, and also explores the use of sets toward a more po...
HYPERSOLVER: A Graphical Tool for Commonsense Set Theory
, 1996
"... This paper investigates an alternative set theory (due to Peter Aczel) called Hyperset Theory. Aczel uses a graphical representation for sets and thereby allows the representation of nonwellfounded sets. A program, called HYPERSOLVER, which can solve systems of equations defined in terms of sets ..."
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Cited by 1 (1 self)
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This paper investigates an alternative set theory (due to Peter Aczel) called Hyperset Theory. Aczel uses a graphical representation for sets and thereby allows the representation of nonwellfounded sets. A program, called HYPERSOLVER, which can solve systems of equations defined in terms of sets in the universe of this new theory is presented. This may be a useful tool for commonsense reasoning. 1 INTRODUCTION Set theory has long occupied a unique place in mathematics since it allows various other branches of mathematics to be formally defined within it. The theory has ignited many debates on its nature and a number of different axiomatizations were developed to formalize its underlying `philosophical' principles. Collecting entities into an abstraction for further thought (i.e., set construction) is an important process in mathematics, and this brings in assorted problems [5]. The theory had many groundshaking crises (like the discovery of the Russell's Paradox [6]) throughout it...
Calibrating, Counting, Grounding, Grouping*
"... Introduction Even an "elementary" intelligence for control of the physical world will require very many kinds of knowledge and ability. Among these are ones related to perception, action, and reasoning about "near space": that region comprising one's body and the portion of space within reach of on ..."
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Introduction Even an "elementary" intelligence for control of the physical world will require very many kinds of knowledge and ability. Among these are ones related to perception, action, and reasoning about "near space": that region comprising one's body and the portion of space within reach of one's effectors; chief among these are individuation and categorization of objects. These in turn are made useful in part by the additional capacities to estimate category size, change one's beliefs about categories, and form new categories or revise old categories. In this position paper we point out some issues in knowledge representation that can arise with respect to the above capacities, and suggest that the framework of "active logics" (see below) may be marshaled toward solutions. We will conduct our discussion in terms of lear'tit9 to utder'statd i a sematicalll explicit wal oe's ow sea, sot'imotor' slstem ad its iteractios with ear'space objects. Implicit in successful grouping (c