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33
Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen's Interval Algebra
 Journal of the ACM
, 1995
"... We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient for deciding satisfiabil ..."
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Cited by 160 (9 self)
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We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient for deciding satisfiability. Further, using an extensive machinegenerated case analysis, we show that the ORDHorn subclass is a maximal tractable subclass of the full algebra (assuming<F NaN> P6=NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations. This work has been supported by the German Ministry for Research and Technology (BMFT) under grant ITW 8901 8 as part of the WIP project and under grant ITW 9201 as part of the TACOS project. 1 1 Introduction Temporal information is often conveyed qualitatively by specifying the relative positions of time intervals such as ". . . point to the figure while explaining the performance of the system . . . "...
Improvements To Propositional Satisfiability Search Algorithms
, 1995
"... ... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable ..."
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Cited by 160 (0 self)
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... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable random 3SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NPcomplete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.
Knowledge compilation and theory approximation
 Journal of the ACM
, 1996
"... Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often t ..."
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Cited by 157 (5 self)
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Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often too restrictive for practical applications, whereas the latter leads to uncertainty about exactly what can and cannot be inferred from the knowledge base. We present a third alternative, in which knowledge given in a general representation language is translated (compiled) into a tractable form — allowing for efficient subsequent query answering. We show how propositional logical theories can be compiled into Horn theories that approximate the original information. The approximations bound the original theory from below and above in terms of logical strength. The procedures are extended to other tractable languages (for example, binary clauses) and to the firstorder case. Finally, we demonstrate the generality of our approach by compiling concept descriptions in a general framebased language into a tractable form.
On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus
 Artificial Intelligence
, 1997
"... The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. ..."
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Cited by 108 (22 self)
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The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NPhard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus" RCC8. We extend Bennett's encoding of RCC8 in modal logic. Based on this encoding, we prove that reasoning is NPcomplete in general and identify a maximal tractable subset of the relations in RCC8 that contains all base relations. Further, we show that for this subset pathconsistency is sufficient for deciding consistency. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. One particular approach in this context has been developed by Randell, Cui, and Cohn [20], the socalled Region Connecti...
Spatial Reasoning with Topological Information
 Ph.D. thesis, Institut fur Informatik, AlbertLudwigsUniversitat Freiburg
, 1998
"... . This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the re ..."
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Cited by 45 (1 self)
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. This chapter summarizes our ongoing research on topological spatial reasoning using the Region Connection Calculus. We are addressing different questions and problems that arise when using this calculus. This includes representational issues, e.g., how can regions be represented and what is the required dimension of the applied space. Further, it includes computational issues, e.g., how hard is it to reason with the calculus and are there efficient algorithms. Finally, we also address cognitive issues, i.e., is the calculus cognitively adequate. 1 Introduction When describing a spatial configuration or when reasoning about such a configuration, often it is not possible or desirable to obtain precise, quantitative data. In these cases, qualitative reasoning about spatial configurations may be used. Different aspects of space can be treated in a qualitative way. Among others there are approaches considering orientation, distance, shape, topology, and combinations of these. A summary o...
Tractable Databases: How to Make Propositional Unit Resolution Complete through Compilation
, 1994
"... We present procedures to compile any propositional clausal database \Sigma into a logically equivalent "compiled" database \Sigma ? such that, for any clause C, \Sigma j= C if and only if there is a unit refutation of \Sigma ? [ :C. It follows that once the compilation process is complete any qu ..."
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Cited by 38 (5 self)
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We present procedures to compile any propositional clausal database \Sigma into a logically equivalent "compiled" database \Sigma ? such that, for any clause C, \Sigma j= C if and only if there is a unit refutation of \Sigma ? [ :C. It follows that once the compilation process is complete any query about the logical consequences of \Sigma can be correctly answered in time linear in the sum of the sizes of \Sigma ? and the query. The compiled database \Sigma ? is for all but one of the procedures a subset of the set P I (\Sigma) of prime implicates of \Sigma, but \Sigma ? can be exponentially smaller than P I (\Sigma). Of independent interest, we prove the equivalence of unitrefutability with two restrictions of resolution, and provide a new sufficient condition for unit refutation completeness, thus identifying a new class of tractable theories, one which is of interest to abduction problems as well. Finally, we apply the results to the design of a complete LTMS. 1 INTRODUCT...
Efficient Algorithms for Qualitative Reasoning about Time
 Artificial Intelligence
, 1995
"... Reasoning about temporal information is an important task in many areas of Artificial Intelligence. In this paper we address the problem of scalability in temporal reasoning by providing a collection of new algorithms for efficiently managing large sets of qualitative temporal relations. We focus on ..."
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Cited by 32 (6 self)
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Reasoning about temporal information is an important task in many areas of Artificial Intelligence. In this paper we address the problem of scalability in temporal reasoning by providing a collection of new algorithms for efficiently managing large sets of qualitative temporal relations. We focus on the class of relations forming the Point Algebra (PArelations) and on a major extension to include binary disjunctions of PArelations (PAdisjunctions). Such disjunctions add a great deal of expressive power, including the ability to stipulate disjointness of temporal intervals, which is important in planning applications. Our representation of time is based on timegraphs, graphs partitioned into a set of chains on which the search is supported by a metagraph data structure. The approach is an extension of the time representation proposed by Schubert, Taugher and Miller in the context of story comprehension. The algorithms herein enable construction of a timegraph from a given set of PAr...
Combining a Logical and a Numerical Method for Data Reconciliation
 in "Journal on Data Semantics", 06 2009, p. 6694, http://hal.inria.fr/inria00433007/en/. gemo 19 International PeerReviewed Conference/Proceedings
"... Abstract. The reference reconciliation problem consists in deciding whether different identifiers refer to the same data, i.e. correspond to the same real world entity. In this article we present a reference reconciliation approach which combines a logical method for reference reconciliation called ..."
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Cited by 20 (6 self)
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Abstract. The reference reconciliation problem consists in deciding whether different identifiers refer to the same data, i.e. correspond to the same real world entity. In this article we present a reference reconciliation approach which combines a logical method for reference reconciliation called L2R and a numerical one called N2R. This approach exploits the schema and data semantics, which is translated into a set of Horn FOL rules of reconciliation. These rules are used in L2R to infer exact decisions both of reconciliation and nonreconciliation. In the second method N2R, the semantics of the schema is translated in an informed similarity measure which is used by a numerical computation of the similarity of reference pairs. This similarity measure is expressed in a non linear equation system, which is solved by using an iterative method. The experiments of the methods made on two different domains, show good results for both recall and precision. They can be used separately or in combination. We have shown that their combination allows to improve runtime performance.
A maximalliteral unit strategy for Horn clauses
 In Proc. CTRS90
, 1991
"... A new positiveunit theoremproving procedure for equational Horn clauses is presented. It uses a term ordering to restrict paxamodulation to potentially maximal sides of equations. Completeness is shown using proof orderings. 1. ..."
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Cited by 16 (0 self)
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A new positiveunit theoremproving procedure for equational Horn clauses is presented. It uses a term ordering to restrict paxamodulation to potentially maximal sides of equations. Completeness is shown using proof orderings. 1.
Combining Topological and Qualitative Size Constraints for Spatial Reasoning
, 1998
"... . Information about the relative size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we combine a simple framework for reasoning about qualitative size relations with the Region Connection Cal ..."
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Cited by 16 (4 self)
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. Information about the relative size of spatial regions is often easily accessible and, when combined with other types of spatial information, it can be practically very useful. In this paper we combine a simple framework for reasoning about qualitative size relations with the Region Connection Calculus RCC8, a widely studied approach for qualitative spatial reasoning with topological relations. Reasoning about RCC8 relations is NPhard, but a large maximal tractable subclass of RCC8 called b H8 was identified. Interestingly, any constraint in RCC8 \Gamma b H8 can be consistently reduced to a constraint in b H8 , when an appropriate size constraint between the spatial regions is supplied. We propose an O(n 3 ) time pathconsistency algorithm based on a novel technique for combining RCC8 constraints and relative size constraints, where n is the number of spatial regions. We prove its correctness and completeness for deciding consistency when the input contains topological ...