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

Audrey P. Ferry
1995 Annals of Mathematics and Artificial Intelligence  
In terms 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.  ... 
doi:10.1007/bf01536400 fatcat:bl533e4egnbznfcv4ykwx35ydq

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

Giovanni Amendola, Thomas Eiter, Michael Fink, Nicola Leone, João Moura
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  ... 
doi:10.1016/j.artint.2016.01.011 fatcat:kgyijjxvanawfpqmmfvnn34v6e

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

Karim Khanaki
2016 Fundamenta Mathematicae  
For 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).  ... 
doi:10.4064/fm208-1-2016 fatcat:w5y7wspwdrbxlpxn45kjh4s6ba

A theory of nonmonotonic rule systems II

W. Marek, A. Nerode, J. Remmel
1992 Annals of Mathematics and Artificial Intelligence  
Our translation 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  ... 
doi:10.1007/bf01543477 fatcat:ndme7xdplfhz5dkyc55o4vtrze

Set Constraints in Logic Programming [chapter]

Victor W. Marek, Jeffrey B. Remmel
2003 Lecture Notes in Computer Science  
Our 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.  ... 
doi:10.1007/978-3-540-24609-1_16 fatcat:otj5g45pmbaujnzhw6k4gt2kzi

Locally Determined Logic Programs and Recursive Stable Models

Douglas Cenzer, Jeffrey B. Remmel, Amy Vanderbilt
2004 Annals of Mathematics and Artificial Intelligence  
In general, 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.  ... 
doi:10.1023/b:amai.0000012868.41613.e7 fatcat:rs3oe3igdzfsdmoblw6vbn7mje

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

Pascal Hitzler, Anthony Karel Seda
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.  ... 
doi:10.1016/s0304-3975(02)00709-0 fatcat:pciqlj67q5dwhi4csdrjqsngc4

Autoepistemic logic

Wiktor Marek, Mirosław Truszczyński
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  ... 
doi:10.1145/116825.116836 fatcat:ngrivoxco5czdfx36etcwcjmoy

Default reasoning using classical logic

Rachel Ben-Eliyahu, Rina Dechter
1996 Artificial Intelligence  
Our procedures allow also for computing 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.  ... 
doi:10.1016/0004-3702(95)00095-x fatcat:cfqq26hb7jfp7henq6m34cbvem

Modular specifications with supernormal defaults

Stefan Brass
1994 Annals of Mathematics and Artificial Intelligence  
Our approach is similar to 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.  ... 
doi:10.1007/bf01530785 fatcat:zlzwo7pqojhw5bdwbrhjlqt6tq

Default Reasoning over Domains and Concept Hierarchies [chapter]

Pascal Hitzler
2004 Lecture Notes in Computer Science  
Rounds 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  ... 
doi:10.1007/978-3-540-30221-6_27 fatcat:3hjbyv545jhrbfkmpl5da5kxfe

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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