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12
Commonsense arithmetic reasoning
 Proceedings of AAAI86
, 1986
"... “Arithmetic reasoning ” can range in complexity from simple integer arithmetic to powerful symbolic algebraic reasoning of the sort done by MACSYMA. We describe an arithmetic reasoning system of intermediate complexity called the Quantity Lattice. In a computationally efficient manner the Quantity ..."
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Cited by 32 (1 self)
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“Arithmetic reasoning ” can range in complexity from simple integer arithmetic to powerful symbolic algebraic reasoning of the sort done by MACSYMA. We describe an arithmetic reasoning system of intermediate complexity called the Quantity Lattice. In a computationally efficient manner the Quantity Lattice integrates qualitative and quantitative reasoning, and combines inequality reasoning with reasoning about simple arithmetic expressions, such as addition or multiplication. The system has proven useful in doing simulation and analysis in several domains, including geology and semiconductor fabrication, by supporting useful forms of reasoning about time and the changes that hap pen when processes occur. 1
Causal Reasoning about Quantities
 Readings in Qualitative Reasoning about Physical Systems
, 1990
"... Causality plays an important role in human thinking. Yet we are far from having a complete account of causal reasoning. This paper presents an analysis of causal reasoning about changes in quantities. We abstract from Al theories of qualitative physics three dimensions along which causal reasoning a ..."
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Cited by 16 (4 self)
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Causality plays an important role in human thinking. Yet we are far from having a complete account of causal reasoning. This paper presents an analysis of causal reasoning about changes in quantities. We abstract from Al theories of qualitative physics three dimensions along which causal reasoning about quantities may be decomposed. We then use this framework to make some psychological predictions. 1.
An Application of Constraint Propagation to DataFlow Analysis
 IN PROC OF NINTH IEEE CONFERENCE ON AI APPLICATIONS
, 1993
"... The optimized compilation of Constraint Logic Programming (CLP) languages can give rise to impressive performance improvements, even more impressive than the ones obtainable for the compilation of Prolog. On the other hand, the global analysis techniques needed to derive the necessary information ca ..."
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Cited by 11 (8 self)
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The optimized compilation of Constraint Logic Programming (CLP) languages can give rise to impressive performance improvements, even more impressive than the ones obtainable for the compilation of Prolog. On the other hand, the global analysis techniques needed to derive the necessary information can be significantly more complicated than in the case of Prolog. The original contribution of the present work is the integration of approximate inference techniques, well known in the field of artificial intelligence (AI), with an appropriate framework for the definition of nonstandard semantics of CLP. This integration turns out to be particularly appropriate for the considered case of the abstract interpretation of CLP programs over numeric domains. One notable advantage of this approach is that it allows to close the often existing gap between the formalization of dataflow analysis in terms of abstract interpretation and the possibility of efficient implementations. Towards this aim we i...
The Logic of Occurrence
, 1987
"... A general problem in qualitative physics is determining the consequences of assumptions about the behavior of a system. If the space of behaviors is represented by an envisionment, many such consequences can be represented by pruning states from the envisionment. This paper provides a formal logic o ..."
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Cited by 10 (3 self)
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A general problem in qualitative physics is determining the consequences of assumptions about the behavior of a system. If the space of behaviors is represented by an envisionment, many such consequences can be represented by pruning states from the envisionment. This paper provides a formal logic of occurrence which justifies the algorithms involved and provides a language for relating specific histories to envisionments. The concepts and axioms are general enough to be applicable to any system of qualitative physics. We further propose the concept of transverse quantities as a general solution to qualitative versions of Zeno's paradox. The utility of these ideas is illustrated by a rational reconstruction of the pruning algorithms used in FROB, a working AI program. December, 1 Introduction A goal of qualitative physics is to predict the behavior of physical systems. One technique, envisioning, generates all possible behaviors of a system, relative to a particular set of backgroun...
Static Analysis of CLP Programs over Numeric Domains
 IN ACTES WORKSHOP ON STATIC ANALYSIS '92
, 1992
"... Constraint logic programming (CLP) is a generalization of the pure logic programming paradigm, having similar modeltheoretic, fixpoint and operational semantics [9]. Since the basic operational step in program execution is a test for solvability of constraints in a given algebraic structure, CLP ha ..."
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Cited by 7 (6 self)
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Constraint logic programming (CLP) is a generalization of the pure logic programming paradigm, having similar modeltheoretic, fixpoint and operational semantics [9]. Since the basic operational step in program execution is a test for solvability of constraints in a given algebraic structure, CLP has in addition an algebraic semantics. CLP is then a general paradigm which may be instantiated on various semantic domains, thus achieving a good expressive power. One relevant feature is the distinction between testing for solvability and computing a solution of a given constraint formula. In the logic programming case, this corresponds to the unification process, which tests for solvability by computing a solution (a set of equations in solved form or most general unifier ). In CLP, the computation of a solution of a constraint is left to a constraint solver, which does not affect the semantic definition of the language. This allows different computational domains, e.g. real arithmetic, to...
The qualitative process engine: A study in assumptionbased truth maintenance
 In Qualitative Reasoning Workshop Abstracts. Qualitative Reasoning Group, University of Illinois at UrbanaChampaign
, 1987
"... This paper describes how to use an assumptionbased truth maintenance system (ATMS) to significantly speed up qualitative reasoning. Specifically, we introduce three organizing abstractions for ATMSbased problem solvers (manyworlds databases, justify/interpret cycles, and closedworld tables). We ..."
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Cited by 4 (0 self)
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This paper describes how to use an assumptionbased truth maintenance system (ATMS) to significantly speed up qualitative reasoning. Specifically, we introduce three organizing abstractions for ATMSbased problem solvers (manyworlds databases, justify/interpret cycles, and closedworld tables). We illustrate their utility by describing the Qualitative Process Engine (qPE), an implementation of Qualitative Process theory that is roughly 95 timesfaster and signficantly simpler than the previous implementation. After analyzing gPE's performance, we draw some general conclusions about the advantages and disadvantages of assumptionbased truth maintenance systems. Program:ENGINEERING
Geocomputing with Geological Field Data: Is there a 'ghost in the machine'?
"... Bedrock geological mapping, like many fieldbased activities in the geosciences, involves the construction of a spatial and temporal model of a region via fieldbased surveys. The geologist interprets the field evidence to constrain possible geologic histories, and constructs hypotheses by combining ..."
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Bedrock geological mapping, like many fieldbased activities in the geosciences, involves the construction of a spatial and temporal model of a region via fieldbased surveys. The geologist interprets the field evidence to constrain possible geologic histories, and constructs hypotheses by combining the field constraints with extant geologic theory. Such reasoning often leads to multiple valid hypotheses since the evidence from field and theory regularly underdetermines the history; consequently there are many valid ways to explain limited data in the Earth's large open system. Because multiple hypotheses can fit the facts, and because the facts themselves are contentious, being somewhat subjective due to the variability of observation and interpretation, geological mappers often regard their skill as an art as well as a science. The encroachment of computer technologies into the field mapping process, and the subsequent availability of digital field data, provides an opportunity to test these claims geocomputationally in order to evaluate the degree of artistry involved in geological mapping. This study specifically investigates the degree of correlation between field data and the geological classes generalized from them. A study area was chosen where several geologists ' data and interpretations were compared, correlated, and contrasted using unsupervised and supervised classification techniques with the selforganising neural map (SOM). Significant challenges in preparing largely qualitative data for the SOM were overcome and are reported. Also reported are correlation
Labeled graph notations for graphical models
, 2004
"... We introduce new diagrammatic notations for probabilistic independence networks (including Bayes nets and graphical models). These notations include new node and link types that allow for natural representation of a wide range of probabilistic data models including complex hierarchical models. The d ..."
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We introduce new diagrammatic notations for probabilistic independence networks (including Bayes nets and graphical models). These notations include new node and link types that allow for natural representation of a wide range of probabilistic data models including complex hierarchical models. The diagrammatic notations also support models defined on variable numbers of complex objects and relationships. Node types include random variable nodes, index nodes, constraint nodes, and an object supernode. Link types include conditional dependency, indexing and index limitation, variable value limitation, and gating a dependency between nodes or objects by an arbitrary graph. Examples are shown for clustering problems, information retrieval, unknown graph structures in biological regulation, and other scientific domains. The diagrams may be taken as a shorthand notation for a more detailed syntactic representation by an algebraic expression for factored probability distributions, which in turn may be specified by stochastic parameterized grammar or graph grammar models. We illustrate these ideas with previously described applications and potential new ones.
Reasoning About Fluids Via Molecular Collections
"... Hayes has identified two distinct ontologies for reasoning about liquids. Most qualitative physics research has focused on applying and generalizing his containedliquid ontology. This paper presents a technique for generating descriptions using the molecular collection (MC) ontology, a specializati ..."
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Hayes has identified two distinct ontologies for reasoning about liquids. Most qualitative physics research has focused on applying and generalizing his containedliquid ontology. This paper presents a technique for generating descriptions using the molecular collection (MC) ontology, a specialization of his alternate ontology which represents liquids in terms of little &quot;pieces of stuff &quot; traveling through a system. We claim that MC descriptions are parasitic on the ContainedStuff ontology, and present rules for generating MC descriptions given a Qualitative Process theory model using contained stuffs. We illustrate these rules using several implemented examples and discuss how this representation can be used to draw cornplex conclusions. I.
UIUCDCSR861300 The Logic of Occurrence
"... A general problem in qualitative physics is determining the consequences of assumptions about the behavior of a system. If the space of behaviors is represented by an envisionment, many such consequences can be represented by pruning states from the envisionment. This paper provides a formal logic o ..."
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A general problem in qualitative physics is determining the consequences of assumptions about the behavior of a system. If the space of behaviors is represented by an envisionment, many such consequences can be represented by pruning states from the envisionment. This paper provides a formal logic of occurrence which justifies the algorithms involved and provides a language for relating specific histories to envisionments. The concepts and axioms are general enough to be applicable to any system of qualitative physics. We further propose the concept of transverse quantities as a general solution to qualitative versions of Zeno's paradox. The utility of these ideas is illustrated by a rational reconstruction of the pruning algorithms used in FROB, a working AI program.