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Erik Sandewall

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19 papers
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19

AIJ Journal 2011 Journal Article

From systems to logic in the early development of nonmonotonic reasoning

  • Erik Sandewall

This note describes how the notion of nonmonotonic reasoning emerged in Artificial Intelligence from the mid-1960's to 1980. It gives particular attention to the interplay between three kinds of activities: design of high-level programming systems for AI, design of truth-maintenance systems, and the development of nonmonotonic logics. This was not merely a development from logic to implementation; in several cases there was a development from a system design to a corresponding logic. The article concludes with some reflections on the roles and relationships between logicist theory and system design in AI, and in particular in Knowledge Representation.

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AIJ Journal 2010 Journal Article

Defeasible inheritance with doubt index and its axiomatic characterization

  • Erik Sandewall

This article introduces and uses a representation of defeasible inheritance networks where links in the network are viewed as propositions, and where defeasible links are tagged with a quantitative indication of the proportion of exceptions, called the doubt index. This doubt index is used for restricting the length of the chains of inference. The representation also introduces the use of defeater literals that disable the chaining of subsumption links. The use of defeater literals replaces the use of negative defeasible inheritance links, expressing “most A are not B”. The new representation improves the expressivity significantly. Inference in inheritance networks is defined by a combination of axioms that constrain the contents of network extensions, a heuristic restriction that also has that effect, and a nonmonotonic operation of minimizing the set of defeater literals while retaining consistency. We introduce an underlying semantics that defines the meaning of literals in a network, and prove that the axioms are sound with respect to this semantics. We also discuss the conditions for obtaining completeness. Traditional concepts, assumptions and issues in research on nonmonotonic or defeasible inheritance are reviewed in the perspective of this approach.

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TIME Conference 2001 Conference Paper

Cellular Ontology as a Basis for Spatiotemporal Reasoning

  • Erik Sandewall

A logic for reasoning about dynamic systems should be defined on three levels. The material level is expressed in quantitative terms, the image level defines models in terms of discrete mathematics, and the logic level defines the logical language and deduction system. Consider the problem of guiding a vehicle that has to move within severe spatial constraints. For a simple version of a cellular ontology, the material level is a 2D surface where vehicles move along trajectories formed from straight-line segments and circular arcs which are each others' tangents at the points of transition. The image level is obtained by dividing the surface into equally-sized cells, which may be, for example, quadratic or hexagonal. For a given cell structure, with a finite set of ports and a finite set of orientations, and allowing also for some restrictions on vehicle movements, we obtain a finite set of possible maneuvers. It is therefore possible to calculate in advance a qualitative information structure that can be used for analyzing and planning the movements of a vehicle in the cellular driving space.

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NMR Workshop 1989 Conference Paper

The Semantics of Non-Monotonic Entailment Defined Using Partial Interpretations

  • Erik Sandewall

Abstract The logic of preferential entailment is generalized to the case where the preference ordering is a part of the models, so that axioms can make statements about the preference ordering, and thereby constrain it. The following technique is used: An aggregate is a pair 〈Δ, ≪〉, where Δ is a set of partial interpretations, and ≪ is a preference order on the members of Δ. A monadic propositional operator D (for default) is introduced, where Dα is satisfied in a member J of Δ in an aggregate 〈Δ, ≪〉 iff α is satisfied in all ≪-minimal completions of J in Δ. A number of examples of the use of this semantics are discussed, and it is shown that default rules can be expressed in such ways that the conclusions dictated by common sense are obtained.

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AAAI Conference 1986 Conference Paper

A Representation of Action Structures

  • Erik Sandewall

We consider structures of actions which are partially ordered for time, which may occur in parallel, and which have lasting effects on the state of the world. Such action structures are of interest for problem-solving with multiple actors, and for understanding narrative texts where several things are going on at the same time. They are also of interest for other branches of computer science besides AI. Actions in the action structure are characterized in terms of preconditions, postconditions, and prevail conditions, where the prevail condition is a requirement on what must hold for the duration of the action. All three conditions are partial states of the world, and therefore elements of a lattice. We develop the formalism, give an example, and specify formally the criterion for admissible action' structures, where postconditions of earlier actions serve as prevail- or preconditions of later actions in a coherent way, and there are no conflicting attempts to change ("update" a feature in the world.

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