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A topological characterization of the stable and minimal model classes of propositional logic programs

1995
*
Annals of Mathematics and Artificial Intelligence
*

In terms

doi:10.1007/bf01536400
fatcat:bl533e4egnbznfcv4ykwx35ydq
*of**the*arithmetic hierarchy,*the*complexity*of**the*set*of**minimal**models**and**of**the*set*of**stable**models**of**a**propositional*general*logic**program*has previously been described. ... set*of**minimal**models**of**a*prerequisite-free*program**and**a**logical*description in terms*of*formulas. ...*The*author would also like to acknowledge useful discussions with Professor David Kueker*of**the*University*of*Maryland concerning definability*of**minimal**models*. ...##
###
Page 558 of Mathematical Reviews Vol. , Issue 97A
[page]

1997
*
Mathematical Reviews
*

:68029 68N17 03B70
Ferry, Audrey P. (1-MI; Ann Arbor, MI)

*A**topological**characterization**of**the**stable**and**minimal**model**classes**of**propositional**logic**programs*. ... Let Min(P)*and*Stab(P) denote*the*set*of**minimal**and**stable**models**of*P. ...##
###
Semi-equilibrium models for paracoherent answer set programs

2016
*
Artificial Intelligence
*

*The*latter has both

*a*transformational

*and*

*a*

*model*-theoretic

*characterization*that reveals it as

*a*relaxation

*of*equilibrium

*logic*,

*the*

*logical*reconstruction

*of*answer set semantics,

*and*is thus called ... In this paper, we give

*a*

*model*-theoretic

*characterization*

*of*semi-

*stable*

*models*, which makes

*the*semantics more accessible. ... Acknowledgments We would like to thank

*the*reviewers

*of*preliminary conference versions

*of*parts

*of*this paper

*and*

*of*this article for their helpful

*and*constructive comments, as well as José Alferes

*and*...

##
###
Page 7797 of Mathematical Reviews Vol. , Issue 2002K
[page]

2002
*
Mathematical Reviews
*

*The*main result

*of*this paper is

*a*

*characterization*

*of*

*the*L}

*classes*

*of*

*models*in terms

*of*ultraproducts

*and*

*topologies*naturally de- finable on ultraproducts. S. R. ...

*The*paper pursues

*the*

*program*

*of*building w-

*stable*expansions

*of*strongly

*minimal*structures according to

*the*strategy developed by Hrushovski to obtain “new” strongly

*minimal*sets. ...

##
###
Amenability, extreme amenability, model-theoretic stability, and dependence property in integral logic

2016
*
Fundamenta Mathematicae
*

For

doi:10.4064/fm208-1-2016
fatcat:w5y7wspwdrbxlpxn45kjh4s6ba
*a**stable*formula ϕ, we prove definability*of*all complete ϕ-types over*models**and*deduce from this*the*fundamental theorem*of*stability. ... First, we study*and**characterize*amenable*and*extremely amenable*topological*semigroups in terms*of*invariant measures using integral*logic*. ... Acknowledgements*The*author is partially supported by grants from IPM, (Nos. 91030032*and*92030032). ...##
###
A theory of nonmonotonic rule systems II

1992
*
Annals of Mathematics and Artificial Intelligence
*

Our translation

doi:10.1007/bf01543477
fatcat:ndme7xdplfhz5dkyc55o4vtrze
*of**propositional**logic**programs*as nonmonotonic rule systems provides an infinitary*characterization**of**the**stable**models**of**logic**programs*. ... So*the*results*of*Jockusch*and*Soare [ 1972a ] apply both to*logic**programming**and*to default*logic*,*and*we get*a*series*of*results in*the*recursion theory*of**stable**models**of**logic**programs*by lifting ...##
###
Set Constraints in Logic Programming
[chapter]

2003
*
Lecture Notes in Computer Science
*

Our

doi:10.1007/978-3-540-24609-1_16
fatcat:otj5g45pmbaujnzhw6k4gt2kzi
*programs*admit atoms*of**the*form X, F where X is*a*finite set*of**propositional*atoms*and*F is an arbitrary family*of*subsets*of*X. ... We call such atoms set constaints*and*show that*the*concept*of**stable**model*can be generalized to*programs*admitting set constraints both in*the*bodies*and**the*heads*of*clauses. ... Acknowledgments*The*first author's research has been partially supported by*the*NSF grants IIS-0097278*and*IIS-0325063. ...##
###
Locally Determined Logic Programs and Recursive Stable Models

2004
*
Annals of Mathematics and Artificial Intelligence
*

In general,

doi:10.1023/b:amai.0000012868.41613.e7
fatcat:rs3oe3igdzfsdmoblw6vbn7mje
*the*set*of**stable**models**of**a*recursive*logic**program*can be quite complex. ... For example, it follows from results*of*Marek, Nerode,*and*Remme [17] that there exists finite predicate*logic**programs**and*recursive*propositional**logic**programs*which have*stable**models*but no hyperarithmetic ... For arbitrary*propositional**logic**programs*,*the*possible sets*of**stable**models*were*characterized*by*A*. Ferry [10] in terms*of*an inverse-Scott*topology*. ...##
###
Page 4740 of Mathematical Reviews Vol. , Issue 94h
[page]

1994
*
Mathematical Reviews
*

Stewart,

*Logical**characterizations**of*bounded query*classes*. I. ... Hoofman, Non-*stable**models**of*linear*logic*(209-220); P. M. W. Knijnenburg*and*F. Nordemann,*A*categorical interpretation*of*partial func- tion*logic**and*Hoare*logic*(229-240); N. K. Kossovsky [N. ...##
###
Generalized metrics and uniquely determined logic programs

2003
*
Theoretical Computer Science
*

*The*introduction

*of*negation into

*logic*

*programming*brings

*the*beneÿt

*of*enhanced syntax

*and*expressibility, but creates some semantical problems. ... Our methods allow

*the*analysis

*of*

*classes*

*of*

*programs*which include

*the*acyclic, locally hierarchical,

*and*acceptable

*programs*, amongst others,

*and*draw on ÿxed-point theorems which apply to generalized ...

*The*atomic

*topology*can be

*characterized*in terms

*of*convergence as follows.

*Proposition*42. ...

##
###
Autoepistemic logic

1991
*
Journal of the ACM
*

*The*theorem

*characterizing*expansions is applied to two

*classes*

*of*theories, K1-theories

*and*se-

*programs*. ... Finally, connections with

*stable*

*model*semantics for

*logic*

*programs*with negation is discussed. In particular, it is proven that

*the*problem

*of*existence

*of*

*stable*

*models*is NP-complete. ... Although, in

*the*case

*of*

*logic*

*programming*, it is desirable to deal with stratified

*programs*(stratification assures

*the*possibility

*of*selecting

*a*specific

*minimal*Herbrand

*model*), in

*the*general case ...

##
###
Default reasoning using classical logic

1996
*
Artificial Intelligence
*

Our procedures allow also for computing

doi:10.1016/0004-3702(95)00095-x
fatcat:cfqq26hb7jfp7henq6m34cbvem
*stable**models**of*extended*logic**programs*. 2 ... is*a*one-to-one correspondence between*models*for*the*latter*and*extensions*of**the*former. ... 92-122, by grants from Toshiba*of*America*and*Xerox P alo Alto research center,*and*by an IBM graduate fellowship to*the*rst author. ...##
###
Modular specifications with supernormal defaults

1994
*
Annals of Mathematics and Artificial Intelligence
*

Our approach is similar to

doi:10.1007/bf01530785
fatcat:zlzwo7pqojhw5bdwbrhjlqt6tq
*the*distinction between head*and*body*of**logic**programming*rules, but it works on*the*higher level*of*default theories. ... This greatly improves*the*understandability*of*large default specifications*and*especially helps to solve*the*problem*of*unwanted contrapositions*of*rules. ... He is also coauthor*of*[BL91] , where we used related ideas to formalize locality in object-oriented specifications. ...##
###
Default Reasoning over Domains and Concept Hierarchies
[chapter]

2004
*
Lecture Notes in Computer Science
*

Rounds

doi:10.1007/978-3-540-30221-6_27
fatcat:3hjbyv545jhrbfkmpl5da5kxfe
*and*G.-Q. Zhang have proposed to study*a*form*of*disjunctive*logic**programming*generalized to algebraic domains [1]. ... disjunctive*logic**programs*. ... Clausal*Logic**and**Logic**Programming*in Algebraic Domains*The*study*of*domain theory from*a**logical*perspective has*a*long tradition,*and*originates from [9] , where*a**logical**characterization*(more precisely ...##
###
Page 491 of Mathematical Reviews Vol. , Issue 94a
[page]

1994
*
Mathematical Reviews
*

We give

*a*geometric*characterization**of**a*similar subset in*the*general case,*and*prove that it is*stable*under composition. ... In*the*case*of*GK,*a*preferred*model*is not simply*a**minimal**model*according to some partial order. ...
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