Logic programming and bisimulation

The logic programming encoding of the set-theoretic graph property known as bisimulation is analyzed. This notion is of central importance in non-well-founded set theory, semantics of concurrency, model checking, and coinductive reasoning. From a modeling point of view, it is particularly interesting since it allows two alternative high-level characterizations. We analyze the encoding style of these modelings in various dialects of Logic Programming. Moreover, the notion also admits a polynomial-time maximum fixpoint procedure that we implemented in Prolog. Similar graph problems which are instead NP hard or not yet perfectly classified (e.g., graph isomorphism) can inherit most from the declarative encodings presented

Introduction to the 28th International Conference on Logic Programming Special Issue

We are proud to introduce this special issue of the Journal of Theory and Practice of Logic Programming (TPLP), dedicated to the full papers accepted for the 28th International Conference on Logic Programming (ICLP). The ICLP meetings started in Marseille in 1982 and since then constitute the main venue for presenting and discussing work in the area of logic programming

Set Unification

The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static analysis, rapid software prototyping. The various solutions proposed are spread across a large literature. In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory. We address the problem of deciding existence of solutions at an abstract level. This provides also the ability to classify different types of set unification problems. Unification algorithms are uniformly proposed to solve the unification problem in each of such classes. The algorithms presented are partly drawn from the literature--and properly revisited and analyzed--and partly novel proposals. In particular, we present a new goal-driven algorithm for general ACI1 unification and a new simpler algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of Logic Programming (TPLP

Planning as Tabled Logic Programming

This paper describes Picat's planner, its implementation, and planning models for several domains used in International Planning Competition (IPC) 2014. Picat's planner is implemented by use of tabling. During search, every state encountered is tabled, and tabled states are used to effectively perform resource-bounded search. In Picat, structured data can be used to avoid enumerating all possible permutations of objects, and term sharing is used to avoid duplication of common state data. This paper presents several modeling techniques through the example models, ranging from designing state representations to facilitate data sharing and symmetry breaking, encoding actions with operations for efficient precondition checking and state updating, to incorporating domain knowledge and heuristics. Broadly, this paper demonstrates the effectiveness of tabled logic programming for planning, and argues the importance of modeling despite recent significant progress in domain-independent PDDL planners.Comment: 27 pages in TPLP 201

3coSoKu and its declarative modeling

In this paper, we analyze the physical puzzle IcoSoKu, a game about placing some given triangular tiles on the faces of an icosahedron in order to fill the capacities of its vertices, and we propose its generalization called 3coSoKu, admitting an arbitrary playing field with triangular faces, arbitrary capacities and an arbitrary set of triangular tiles. First, we prove the strong NP-completeness of 3coSoKu, even when the playing field is a convex polyhedron with equilateral triangles as faces. Second, we encode 3coSoKu both in the constraint modeling language MiniZinc and in the logic programming paradigm known as Answer Set Programming and we develop a visual tool for an accessible interface to the solver. Finally, we use our encodings to verify experimentally that every initial state for IcoSoKu admits a solution.Peer reviewe

Operational and abstract semantics of the query language G-Log

The amount and variety of data available electronically have dramatically increased in the led decade; however, data and documents are stored in different ways and do notusual# show their internal structure. In order to take ful advantage of thetopolk9dQ# structure ofdigital documents, andparticulIII web sites, theirhierarchical organizationshouliz explizatio introducing a notion of querysimil; to the one usedin database systems. A good approach, in that respect, is the one provided bygraphical querylrydM#99; original; designed to model object bases and lndd proposed for semistructured data, la, G-Log. The aim of this paper is to providesuitabl graph-basedsemantics to thislisd;BI# supporting both data structure variabil#I andtopol#Ik;M similpol#I between queries and document structures. A suite ofoperational semantics basedon the notion ofbisimulQM#I is introduced both at theconcr--h level (instances) andat theabstru( level (schemata), giving rise to a semantic framework that benefits from the cross-fertil9;dl of tool originalM designed in quite different research areas (databases, concurrency,loncur static analysis)

MASP-Reduce: A Proposal for Distributed Computation of Stable Models

There has been an increasing interest in recent years towards the development of efficient solvers for Answer Set Programming (ASP) and towards the application of ASP to solve increasing more challenging problems. In particular, several recent efforts have explored the issue of scalability of ASP solvers when addressing the challenges caused by the need to ground the program before resolution. This paper offers an alternative solution to this challenge, focused on the use of distributed programming techniques to reason about ASP programs whose grounding would be prohibitive for mainstream ASP solvers. The work builds on a proposal of a characterization of answer set solving as a form of non-standard graph coloring. The paper expands this characterization to include syntactic extensions used in modern ASP (e.g., choice rules, weight constraints). We present an implementation of the solver using a distributed programming framework specifically designed to manipulate very large graphs, as provided by Apache Spark, which in turn builds on the MapReduce programming framework. Finally, we provide a few preliminary results obtained from the first prototype implementation of this approach