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Logic programming with sets

Gabriel M. Kuper
1990 Journal of computer and system sciences (Print)  
In order to do this, we need to have some way to deal with complex objects in logic programs. Some types of data structures can be easily represented by Prolog structures.  ...  ., forming sets of objects, cannot. Therefore, if we are to use a logic programming language as a query language for nested relations, the language has to be extended to handle sets of objects.  ...  COMPARISON WITH OTHER WAYS OF ADDING SETS TO LOGIC PROGRAMMING We compare our approach to other ways of adding sets to logic programs, specifically that of LDL [BNR*87] .  ... 
doi:10.1016/0022-0000(90)90033-h fatcat:3yp7r46uinct5dbi3xfbqeyc4a

Logic programming with infinite sets

Douglas Cenzer, Jeffrey B Remmel, Victor W. Marek
2005 Annals of Mathematics and Artificial Intelligence  
Using the ideas from current investigations in Knowledge Representation we study the use of a class of logic programs for reasoning about infinite sets.  ...  Our programs reason about the codes for various infinite sets.  ...  However, we first recall the basic definitions of answer set programming and some of its recent extensions such as logic programming with weight and cardinality constraints [34] and set constraint logic  ... 
doi:10.1007/s10472-005-7030-5 fatcat:veh2e26r7jgwlntmu54nlyp2ay

Answer set programming with default logic

Victor W. Marek, Jeffrey B. Remmel
2004 Non-Monotonic Reasoning  
We develop an Answer Set Programming formalism based on Default Logic. We show that computing generating sets of extensions in this formalism captures all Σ P 2 search problems.  ...  However, one can easily extend the ideas of answer set programming to other nonmonotonic logic formalisms such as default logic (Reiter 1980) .  ...  In section II, we shall describe specifying our formulation of an Answer Set Programming based on default logic.  ... 
dblp:conf/nmr/MarekR04 fatcat:dxb5ejrvgzcojei4n2jdsy2b34

Integrating Cardinality Constraints into Constraint Logic Programming with Sets [article]

Maximiliano Cristiá, Gianfranco Rossi
2021 arXiv   pre-print
The Constraint Logic Programming tool log provides a decision procedure for deciding the satisfiability of formulas involving very general forms of finite sets, without cardinality.  ...  In this paper we adapt and integrate a decision procedure for a theory of finite sets with cardinality into log. The proposed solver is proved to be a decision procedure for its formulas.  ...  Hence, it is difficult to compare the expressiveness of Alberti's logic with other logics analyzed in this section and with ours.  ... 
arXiv:2102.05422v2 fatcat:rjf7pzwt2bepfbpwcbz6b2b2ty

Adding partial functions to Constraint Logic Programming with sets

2015 Theory and Practice of Logic Programming  
In this paper we propose to add partial functions as a primitive feature to a Constraint Logic Programming (CLP) language, namely {log}.  ...  safely deal with.  ...  {log} {log} is a Constraint Logic Programming (CLP) language, whose constraint domain is that of hereditarily finite sets-i.e., finitely nested sets that are finite at each level of nesting.  ... 
doi:10.1017/s1471068415000290 fatcat:5tb7tm3mgbc65cmsrkbrch2e4q

Extending Conceptual Logic Programs with Arbitrary Rules

Stijn Heymans, Davy Van Nieuwenborgh, Dirk Vermeir
2005 Answer Set Programming  
We present extended conceptual logic programs (ECLPs), for which reasoning is decidable and, moreover, can be reduced to finite answer set programming.  ...  ECLPs are useful to reason with both ontological and rule-based knowledge, which is illustrated by simulating reasoning in an expressive description logic (DL) equipped with DL-safe rules.  ...  Answer Set Programming with Open Domains Answer set programming (ASP) [3] is a logic programming paradigm where knowledge is represented by programs and answer sets provide for the intended semantics  ... 
dblp:conf/asp/HeymansNV05 fatcat:hn4tcl37e5aobjaivflyg6okiy

Answer Set Programming with Epistemic Defaults

Shutao Zhang, Zhizheng Zhang, Jun Shen
2021 International Conference on Logic Programming  
The latter extends Epistemic Specification (ES) with an epistemic operator A preceding a literal to express the literal is permitted to be true in some belief sets.  ...  Answer Set Prolog (ASP) and its extensions are considered powerful tools for encoding defaults.  ...  Usually, a non-ground logic program, which is a logic program with variables, is considered as a shorthand for the corresponding ground program.  ... 
dblp:conf/iclp/ZhangZS21 fatcat:5a2pgqk4infafpml4vqougwuxu

Answer Set Programming with External Sources

Christoph Redl, Marc Herbstritt
2012 International Conference on Logic Programming  
Programs with External Source Access (FWF P24090), which gave me the opportunity to work on this interesting topic.  ...  Programs with External Source Access (FWF P24090), in denen ich während meines Doktoratsstudiums arbeiten durfte.  ...  Logic Programs with Function Symbols.  ... 
doi:10.4230/lipics.iclp.2012.469 dblp:conf/iclp/Redl12 fatcat:2yxyy6gqzrforanlqayak5cvxq

Paraconsistent Logic Programs with Four-Valued Rough Sets [chapter]

Jan Małuszyński, Andrzej Szałas, Aida Vitória
2008 Lecture Notes in Computer Science  
This paper presents a language for defining four-valued rough sets and to reason about them. Our framework brings together two major fields: rough sets and paraconsistent logic programming.  ...  Our language allows the user to define similarity relations and use the approximations induced by them in the definition of other four-valued sets.  ...  We now briefly compare our work with some of the work in the field of paraconsistent logic programming 1 .  ... 
doi:10.1007/978-3-540-88425-5_5 fatcat:g4mkxinvmfdqdgxyk2tqopzsgm

{log}: A language for programming in logic with finite sets

Agostino Dovier, Eugenio G. Omodeo, Enrico Pontelli, Gianfranco Rossi
1996 The Journal of Logic Programming  
An extended logic programming language is presented, that embodies the fundamental form of set designation based on the (nesting) element insertion operator.  ...  A unification algorithm that can cope with set terms is developed and proved correct and terminating.  ...  We have enjoyed useful discussions with Gopal Gupta, Mario Rodr/guez-Artalejo, and Alberto Policriti, who contributed to the axiomatization.  ... 
doi:10.1016/0743-1066(95)00147-6 fatcat:modbseh76vfixdevog746xwjgy

Solving B Constraints with Goal-directed Answer Set Programming

Alexandros Efremidis
2021 International Conference on Logic Programming  
In particular, I develop a framework translating B predicates to s(CASP), a goal-directed form of Answer Set Programming.  ...  This work poses a foundation for future development regarding the translation of B predicates to goal-directed Answer Set Programming and s(CASP) specifically.  ...  Answer Set Programming and s(CASP) Answer Set Programming (ASP) is a form of declarative logic programming, which is primarily oriented towards NP-hard search problems [9] .  ... 
dblp:conf/iclp/Efremidis21 fatcat:74wlmqd4nfdsjcq6d56f3a4gvi

Modelling Grammar Constraints with Answer Set Programming

Christian Drescher, Toby Walsh, Marc Herbstritt
2011 International Conference on Logic Programming  
In this paper, we present answer set programming (ASP) models for an important and very general class of constraints, including all constraints specified via grammars or automata that recognise some formal  ...  Acknowledgements We would like to thank Claude-Guy Quimper and Nina Narodytska for providing us with the benchmark data.  ...  Background Answer Set Programming A (normal) logic program over a set of primitive propositions A, ⊥ ∈ A, is a finite set of rules r of the form a 0 ← a 1 , .., a m , not a m+1 , .., not a n where a  ... 
doi:10.4230/lipics.iclp.2011.28 dblp:conf/iclp/DrescherW11 fatcat:ero2pmifrfcrdjsrblqmosbweq

Incremental Answer Set Programming with Overgrounding

2019 Theory and Practice of Logic Programming  
We focus on the possibility of generating incrementally larger ground logic programs equivalent to a given non-ground one; so called overgrounded programs can be reused in combination with deliberately  ...  Notably, the proposed approach works "under the hood", relieving designers of logic programs from controlling technical aspects of grounding engines and answer set systems.  ...  After submitting a load request for a logic program P along with an initial set of facts F 1 , EA can ask to compute the answer sets of P over F 1 : the Grounder component is in charge of producing and  ... 
doi:10.1017/s1471068419000292 fatcat:cnmg4kkd5zebzgzjzcelk2sete

Open answer set programming with guarded programs

Stijn Heymans, Davy Van Nieuwenborgh, Dirk Vermeir
2008 ACM Transactions on Computational Logic  
Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program's constants.  ...  Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (µ(L)GF).  ...  OPEN ANSWER SET PROGRAMMING WITH GENERALIZED LITERALS In this section, we extend the language of logic programs with generalized literals and modify the open answer set semantics to accommodate for those  ... 
doi:10.1145/1380572.1380575 fatcat:4czeusi3pjh6jlxga3k4fjrjje

ASP (): Answer Set Programming with Algebraic Constraints

2020 Theory and Practice of Logic Programming  
Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP  ...  They extend some of them and provide a generic framework for defining programs with algebraic computation, which can be fruitfully used e.g. for provenance semantics of datalog programs.  ...  Introduction Answer Set Programming (ASP) is a well-known non-monotonic declarative programming paradigm.  ... 
doi:10.1017/s1471068420000393 fatcat:havbpg5bcbfefoaurzksggd7ce
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