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Computing intersections of Horn theories for reasoning with models

Thomas Eiter, Toshihide Ibaraki, Kazuhisa Makino
1999 Artificial Intelligence  
In particular, we show that a model of the intersection Σ of Horn theories Σ 1 , . . . , Σ l , represented by their characteristic models, can be found in linear time, and that some characteristic model  ...  We present low-order polynomial time algorithms or prove intractability for the major computation problems in the context of knowledge bases which are Horn theories.  ...  Acknowledgement The authors are grateful to the anonymous referees for their comments on this paper, pointing out corrections and providing helpful suggestions for improvements; the last paragraph of Section  ... 
doi:10.1016/s0004-3702(99)00021-1 fatcat:4kac2myuovha3pccrk3juby3gm

Horn approximations of empirical data

Henry Kautz, Michael Kearns, Bart Selman
1995 Artificial Intelligence  
Finally, w e discuss algorithms for generating e cient representations of the Horn theory that best approximates a general set of models.  ...  More speci cally, w e examine model-based representations of Horn theories, and show that there are large Horn theories that can be exactly represented by a n exponentially smaller set of characteristic  ...  Acknowledgement We thank Rina Dechter and Judea Pearl for many i n teresting discussions and comments.  ... 
doi:10.1016/0004-3702(94)00072-9 fatcat:wdvnghwvfveddpowjsgrxjhl7q

Page 1452 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
(J-K YOTGI-AMP; Kyoto); Makino, Kazuhisa (J-OSAKEGE-HS; Suita) Computing intersections of Horn theories for reasoning with models.  ...  In 68 COMPUTER SCIENCE 1452 particular, we show that a model of the intersection 2 of Horn theories 2),---,2,, represented by their characteristic models, can be found in linear time, and that some characteristic  ... 

Reasoning with models

Roni Khardon, Dan Roth
1996 Artificial Intelligence  
Moreover, we show that the theory developed here generalizes the model-based approach to reasoning with Horn expressions and captures even the notion of reasoning with Horn approximations.  ...  In addition, we consider the model-based approach to abductive reasoning and show that for any propositional KB, reasoning with its model-based representation yields an abductive explanation in time that  ...  Acknowledgements We wish to thank Les Valiant for helpful discussions and comments.  ... 
doi:10.1016/s0004-3702(96)00006-9 fatcat:x2g65ssvmvgenjdsnrwttubg5q

Page 6171 of Mathematical Reviews Vol. , Issue 94k [page]

1994 Mathematical Reviews  
Several applications of these ideas are described, includ- ing (1) an interpretation of negation-as-failure, (2) a formalization of indefinite reasoning with definite rules, and (3) a methodology for analyzing  ...  (English summary) Fundamentals of computation theory (Szeged, 1993), 162-170, Lecture Notes in Comput. Sci., 710, Springer, Berlin, 1993.  ... 

Why Horn formulas matter in computer science: Initial structures and generic examples [chapter]

J. A. Makowsky
1985 Lecture Notes in Computer Science  
Q-Horn theories in terms of the existence of initial, or equivalently, 3 +-generic pseudo-term models (Theorem 5.9).  ...  This property (admitting initialterm models, admitting A-generic models) garantees that (i) the "closed-world assumption" for databases and "negation as failure" for logic programming are reasonable concepts  ...  We only propose an explanatory paradigm: If there are reasons that the existence of initial models, 3 +-generic models, are crucial for the activity one has in mind then the restriction to Horn formulas  ... 
doi:10.1007/3-540-15198-2_24 fatcat:tahpgd2jnzfy3ajlpktuvauuvi

Why horn formulas matter in computer science: Initial structures and generic examples

J.A. Makowsky
1987 Journal of computer and system sciences (Print)  
Q-Horn theories in terms of the existence of initial, or equivalently, 3 +-generic pseudo-term models (Theorem 5.9).  ...  This property (admitting initialterm models, admitting A-generic models) garantees that (i) the "closed-world assumption" for databases and "negation as failure" for logic programming are reasonable concepts  ...  We only propose an explanatory paradigm: If there are reasons that the existence of initial models, 3 +-generic models, are crucial for the activity one has in mind then the restriction to Horn formulas  ... 
doi:10.1016/0022-0000(87)90027-4 fatcat:idudkigcd5a4zd2uumhnqewzqm

On Horn Axiomatizations for Sequential Data [chapter]

José L. Balcázar, Gemma Casas-Garriga
2004 Lecture Notes in Computer Science  
conditions; these ensure the consistency of the propositional theory obtained with the ordered context.  ...  We prove that our proposed rules can be formally justified by a purely logical characterization, namely, a natural notion of empirical Horn approximation for ordered data which involves background Horn  ...  Given a propositional theory T , there is exactly one minimal Horn theory containing it. Semantically, it contains all the models that are intersections of models of T .  ... 
doi:10.1007/978-3-540-30570-5_15 fatcat:z5k5u2t6xrhrnjf7vzxlwsmq5m

Abduction and the Dualization Problem [chapter]

Thomas Eiter
2003 Lecture Notes in Computer Science  
While computing some abductive explanation for a literal χ with respect to a set of abducibles A from a Horn propositional theory Σ is intractable under the traditional representation of Σ by a set of  ...  For any model v and any set of models M , let max v (M ) denote the set of all the models in M that is maximal with respect to ≤ v . Here, for models w and u, we write Proposition 10.  ...  Complexity of computing all abductive explanations for a query from a Horn theory characteristic models char k+1 (Σ) with respect to (k + 1)-quasi Horn functions will do, which are those functions with  ... 
doi:10.1007/978-3-540-39624-6_1 fatcat:p6i444qsnrazlfezvewhi2b2hu

Page 2195 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews  
Summary: “This paper studies functional dependencies in Horn theories, both when the theory is represented by its clausal form and when it is defined as the Horn envelope of a set of models.  ...  They compare the canon- ical model for S5,,(CDE) with so-called standard models in terms of certain first-order properties.  ... 

Page 1202 of Mathematical Reviews Vol. , Issue 94c [page]

1994 Mathematical Reviews  
The reason for this symmetry is that model elimination treats positive literals and negative literals in the same way.”  ...  Summary: “Recently there has been much interest in the problem of finding the computational content of classical reasoning.  ... 

From Quantitative Spatial Operator to Qualitative Spatial Relation Using Constructive Solid Geometry, Logic Rules and Optimized 9-IM Model, A Semantic Based Approach [article]

Helmi Ben Hmida, Frank Boochs
2013 arXiv   pre-print
In this work, these operators are used to compute topological relations between objects defined by the constraints of the nine Intersection Model (9-IM) from Egenhofer.  ...  The Constructive Solid Geometry (CSG) is a data model providing a set of binary Boolean operators such as Union, Difference and Intersection.  ...  Topological relationships Spatial reasoning is a process that uses spatial theory and artificial intelligence to model and to analyze spatial relations between objects.  ... 
arXiv:1301.4780v1 fatcat:go5nn5wfvbgztd63q5c5xpis3y

Page 4959 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
, Toshihide (J-K YOTGI-AMP; Kyoto); Makino, Kazuhisa (J-OSAKTGE-HS; Toyonaka) Computing intersections of Horn theories for reasoning with models.  ...  We also consider an extension of Horn theories, for which negative results are ob- tained. They indicate that generalizing the positive results beyond Horn theories is not immediate.”  ... 

Translating between Horn Representations and their Characteristic Models [article]

R. Khardon
1995 arXiv   pre-print
Namely, translating is equivalent to deciding whether a given set of models is the set of characteristic models for a given Horn expression.  ...  Characteristic models are an alternative, model based, representation for Horn expressions.  ...  Acknowledgements I am grateful to Thomas Eiter, Heikki Mannila, and Dan Roth for their comments which lead to some of the results in this paper.  ... 
arXiv:cs/9512105v1 fatcat:daz2af564zdqvjv5pllog7lm7u

Disjunctions of Horn Theories and Their Cores

Thomas Eiter, Toshihide Ibaraki, Kazuhisa Makino
2001 SIAM journal on computing (Print)  
The problems are investigated for different representations of Horn theories, namely for Horn CNFs and characteristic models.  ...  In particular, we consider deciding whether a disjunction of Horn theories is Horn, and, if not, computing a Horn core, i.e., a maximal Horn theory included in this disjunction.  ...  We thank the referees for their helpful suggestions, and gratefully acknowledge the partial support of the Scientific Grant in Aid by the Ministry of Education, Science and Culture of Japan (Grant 06044112  ... 
doi:10.1137/s0097539799350840 fatcat:rl5yqkpcpve6fpnj2eudbb7nu4
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