Papers by Luca Bortolussi
We propose a parametric introduction of intensionally defined sets into any CLP (D) CLP (\ mathca... more We propose a parametric introduction of intensionally defined sets into any CLP (D) CLP (\ mathcal {D\}) language. The result is a language CLP (D) CLP (\ mathcal {D\}), where constraints over sets of elements of D\ mathcal D and over sets of sets of elements, and so on, can be expressed. The semantics of CLP (D) CLP (\ mathcal {D\}) is based on the semantics of logic programs with aggregates and the semantics of CLP over sets.
Abstract In this paper we propose a semantically well-founded combination of the constraint solve... more Abstract In this paper we propose a semantically well-founded combination of the constraint solvers used in the constraint programming languages CLP (SET) and CLP (FD). This work demonstrates that it is possible to provide efficient executions (through CLP (FD) solvers) while maintaining the expressive power and flexibility of the CLP (SET) language. We develop a combined constraint solver and we show how static analysis can help in organizing the distribution of constraints to the two constraint solvers.
Abstract We compare two (apparently) rather different set-based constraint languages, and we show... more Abstract We compare two (apparently) rather different set-based constraint languages, and we show that, in spite of their different origins and aims, there are large classes of constraint formulae for which both proposals provide suitable procedures for testing constraint satisfiability with respect to a given privileged interpretation.
Abstract This paper presents the design, implementation and application of a constraint programmi... more Abstract This paper presents the design, implementation and application of a constraint programming framework on 3D crystal lattices. The framework provides the flexibility to express and resolve constraints dealing with structural relationships of entities placed in a 3D lattice structure in space.
Sets and constraint logic programming
Abstract In this paper we present a study of the problem of handling constraints made by conjunct... more Abstract In this paper we present a study of the problem of handling constraints made by conjunctions of positive and negative literals based on the predicate symbols=,∈,∪ and &dvbm0;(ie, disjointness of two sets) in a (hybrid) universe of finite sets. We also review and compare the main techniques considered to represent finite sets in the context of logic languages.
Abstract Constructive negation has been proved to be a valid alternative to negation as failure, ... more Abstract Constructive negation has been proved to be a valid alternative to negation as failure, especially when negation is required to have, in a sense, anactive'role. In this paper we analyze an extension of the original constructive negation in order to gracefully integrate with the management of set-constraints in the context of a Constraint Logic Programming Language dealing with nite sets.
{log}: A language for programming in logic with finite sets
An extended logic programming language is presented, that embodies the fundamental form of set de... more An extended logic programming language is presented, that embodies the fundamental form of set designation based on the (nesting) element insertion operator. The kind of sets to be handled is characterized both by adaptation of a suitable Herbrand universe and via axioms. Predicates ϵ and= designating set membership and equality are included in the base language, along with their negative counterparts∉ and≠. A unification algorithm that can cope with set terms is developed and proved correct and terminating.
Ъ в Й з Ынб га з бйа и гв Д в Хг а в Е
Abstract In this paper we propose an eЦcient symbolic algorithm for the problem of determining th... more Abstract In this paper we propose an eЦcient symbolic algorithm for the problem of determining the maximum bisimulation on a finite structure. The starting point is an algorithm, on explicit representation of graphs, which saves both time and space exploiting the notion of rank. This notion provides a layering of the input model and allows to proceed bottom-up in the bisimulation computation.
Embedding finite sets in a logic programming language
A way of introducing simple (finite) set designations and operations as firstclass objects of an ... more A way of introducing simple (finite) set designations and operations as firstclass objects of an (unrestricted) logic programming language is discussed from both the declarative and the operational semantics viewpoint First, special set terms are added to definite Horn clause logic and an extended Herbrand Universe based on an axiomatic characterization of the kind of sets we are dealing with is defined accordingly.
A fast bisimulation algorithm
In this paper we propose an efficient algorithmic solution to the problem of determining a Bisimu... more In this paper we propose an efficient algorithmic solution to the problem of determining a Bisimulation Relation on a finite structure. Starting from a set-theoretic point of view we propose an algorithm that optimizes the solution to the Relational coarsest Partition problem given by Paige and Tarjan in 1987 and its use in model-checking packages is briefly discussed and tested. Our algorithm reaches, in particular cases, a linear solution.
Minimal set unification
A unification algorithm is said to be minimal for a unification problem if it generates exactly a... more A unification algorithm is said to be minimal for a unification problem if it generates exactly a complete set of minimal unifiers, without instances, without repetitions. Aim of this paper is to describe a new set unification algorithm minimal for a significant collection of sample problems that can be used as benchmarks for testing any set unification algorithm. To this end, a deep combinatorial study for such problems has been realized.
Embedding extensional finite sets in CLP
Abstract In this paper we review the de nition of flogg1, a logic language with sets, from the vi... more Abstract In this paper we review the de nition of flogg1, a logic language with sets, from the viewpoint of CLP. We show that starting with a CLP-scheme allows a more uniform treatment of the built-in set operations (namely,=, 2 and their negative counterparts), and allows all the theoretical results of CLP to be immediately exploitable. We prove this by precisely de ning the privileged interpretation domain and the axioms of the selected set theory.
Problems and solutions related to the introduction of finite set formers and basic operations on ... more Problems and solutions related to the introduction of finite set formers and basic operations on sets in a Logic Programming language are discussed. In particular it is shown that a good solution is to begin with a CLP-scheme whose signature is endowed with two functional symbols: Ø for the empty set and with for the set construction symbol, using the symbols,,=, as constraint predicate symbols.
This paper presents experimental comparisons between declarative encodings of various computation... more This paper presents experimental comparisons between declarative encodings of various computationally hard problems in both Answer Set Programming (ASP) and Constraint Logic Programming (CLP) over finite domains. The objective is to identify how the solvers in the two domains respond to different problems, highlighting strengths and weaknesses of their implementations and suggesting criteria for choosing one approach versus the other.
This paper presents experimental comparisons between the declarative encodings of various computa... more This paper presents experimental comparisons between the declarative encodings of various computationally hard problems in Answer Set Programming (ASP) and Constraint Logic Programming over Finite Domains (CLP (FD)). The objective is to investigate how solvers in the two domains respond to different problems, highlighting the strengths and weaknesses of their implementations, and suggesting criteria for choosing one approach over the other.
The subgraph bisimulation problem
Abstract We study the complexity of the Subgraph Bisimulation Problem, which relates to Graph Bis... more Abstract We study the complexity of the Subgraph Bisimulation Problem, which relates to Graph Bisimulation as Subgraph Isomorphism relates to Graph Isomorphism, and we prove its NP-Completeness. Our analysis is motivated by its applications to semistructured databases.
GASP: Answer set programming with lazy grounding
In recent years, Answer Set Programming has gained popularity as a viable paradigm for applicatio... more In recent years, Answer Set Programming has gained popularity as a viable paradigm for applications in knowledge representation and reasoning. This paper presents a novel methodology to compute answer sets of an answer set program. The proposed methodology maintains a bottom-up approach to the computation of answer sets (as in existing systems), but it makes use of a novel structuring of the computation, that originates from the non-ground version of the program.
On the Representation and Management of Finite Sets in CLP-languages
Abstract We review and compare the main techniques considered to represent finite sets in logic l... more Abstract We review and compare the main techniques considered to represent finite sets in logic languages. We present a technique that combines the benefits of the previous techniques, avoiding their drawbacks. We show how to verify satisfiability of any conjunction of (positive and negative) literals based on=, C, G, and U, n,\, and||, viewed as predicate symbols, in a (hybrid) universe of finite sets. We also show that U and||(ie, disjointness of two sets) are sufficient to represent all the above mentioned operations.
Fast (hyper) set equivalence
One of the main features of intuitive Set Theory is the well-foundedness of membership. As a cons... more One of the main features of intuitive Set Theory is the well-foundedness of membership. As a consequence, standard axiomatic set theories include the foundation axiom that implies that the membership relation forms no cycles or in nite descending chains. In the eighties the necessity to consider theories non assuming this strong constraint (re-) emerged in many communities. Various proposals for non well-founded set theories (and universes) were developed (see, eg, 6]).
On T logic programming
Abstract T-resolution parametrically generalizes standard resolution with respect to a first-orde... more Abstract T-resolution parametrically generalizes standard resolution with respect to a first-order theory T (the parameter). The inherent power of its derivation rule, however, makes it difficult to develop efficient unrestricted T-resolution based systems. CLP (X) parametrically extends Horn clause logic programming with respect to a domain of computation X. The theory T underlying the domain X is fixed a-priori and can not be modified (extended) by the user.
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Papers by Luca Bortolussi