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Computing intersections of Horn theories for reasoning with models

1999
*
Artificial Intelligence
*

In particular, we show that a

doi:10.1016/s0004-3702(99)00021-1
fatcat:4kac2myuovha3pccrk3juby3gm
*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 ...##
###
Horn approximations of empirical data

1995
*
Artificial Intelligence
*

Finally, w e discuss algorithms

doi:10.1016/0004-3702(94)00072-9
fatcat:wdvnghwvfveddpowjsgrxjhl7q
*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. ...##
###
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

1996
*
Artificial Intelligence
*

Moreover, we show that the

doi:10.1016/s0004-3702(96)00006-9
fatcat:x2g65ssvmvgenjdsnrwttubg5q
*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. ...##
###
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]

1985
*
Lecture Notes in Computer Science
*

Q-

doi:10.1007/3-540-15198-2_24
fatcat:tahpgd2jnzfy3ajlpktuvauuvi
*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 ...##
###
Why horn formulas matter in computer science: Initial structures and generic examples

1987
*
Journal of computer and system sciences (Print)
*

Q-

doi:10.1016/0022-0000(87)90027-4
fatcat:idudkigcd5a4zd2uumhnqewzqm
*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 ...##
###
On Horn Axiomatizations for Sequential Data
[chapter]

2004
*
Lecture Notes in Computer Science
*

conditions; these ensure the consistency

doi:10.1007/978-3-540-30570-5_15
fatcat:z5k5u2t6xrhrnjf7vzxlwsmq5m
*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 . ...##
###
Abduction and the Dualization Problem
[chapter]

2003
*
Lecture Notes in Computer Science
*

While

doi:10.1007/978-3-540-39624-6_1
fatcat:p6i444qsnrazlfezvewhi2b2hu
*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*...##
###
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]

2013
*
arXiv
*
pre-print

In this work, these operators are used to

arXiv:1301.4780v1
fatcat:go5nn5wfvbgztd63q5c5xpis3y
*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. ...##
###
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]

1995
*
arXiv
*
pre-print

Namely, translating is equivalent to deciding whether a given set

arXiv:cs/9512105v1
fatcat:daz2af564zdqvjv5pllog7lm7u
*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. ...##
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Disjunctions of Horn Theories and Their Cores

2001
*
SIAM journal on computing (Print)
*

The problems are investigated

doi:10.1137/s0097539799350840
fatcat:rl5yqkpcpve6fpnj2eudbb7nu4
*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 ...
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