ABSTRACT. Answer set programming (ASP) is a declarative language for nonmonotonic reasoning based on stable model semantics, where stable models are classical models of the input program satisfying a stability condition: only necessary information is included in each of these models under the assumptions provided by the model itself for the unknown knowledge in the program, where unknown knowledge is encoded by means of default negation. Reasoning in presence of unknown knowledge is common for rational agents acting in the real world. It is also common that real world agents cannot meet all their desiderata, and therefore ASP programs may come with soft literals for representing numerical preferences over jointly incompatible conditions. Stable models are therefore associated with a cost given by the number of the unsatisfied soft literals, so that stable models of minimum cost are preferred. In this talk I will show algorithms and strategies for computing optimal stable models, discuss their properties and explain how they can be extended to handle some qualitative preferences.

ABSTRACT. In a recent paper by Harrison et al., the concept of program completion is extended to a large class of programs in the input language of the ASP grounder gringo. We would like to automate the process of generating and simplifying completion formulas for programs in that language, because examining the output produced by this kind of software may help programmers to see more clearly what their program does and to what degree its set of stable models conforms with their intentions. If a formal specification for the program is available, then it may be possible to use this software, in combination with automated reasoning tools, to verify that the program is correct. This note is a preliminary report on a project motivated by this idea.

ABSTRACT. Recent research in extensions of Answer Set Programming has included a renewed interest in the language of Epistemic Specifications, which adds modal operators K ("known") and M ("may be true") to provide for more powerful introspective reasoning and enhanced capability, particularly when reasoning with incomplete information. An epistemic logic program is a set of rules in this language. Infused with the research has been the desire for an efficient solver to enable the practical use of such programs for problem solving. In this paper, we report on the current state of development of epistemic logic program solvers.

ABSTRACT. Epistemic Logic Programs (ELPs) are an extension of Answer Set Programming (ASP) with epistemic operators that allow for a form of meta-reasoning, that is, reasoning over multiple possible worlds. Existing ELP solving approaches generally rely on making multiple calls to an ASP solver in order to evaluate the ELP. However, in this paper, we show that there also exists a direct translation from ELPs into non-ground ASP with bounded arity. The resulting ASP program can thus be solved in a single shot. We then implement this encoding method, using recently proposed techniques to handle large, non-ground ASP rules, into a prototype ELP solving system called selp. This solver exhibits competitive performance on a set of ELP benchmark instances.

ABSTRACT. In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by multiplying interpretation vectors and program matrices. To optimize computation in vector spaces, we provide a method of partial evaluation of programs using linear algebra. Partial evaluation is done by unfolding rules in a program, and it is realized in a vector space by multiplying program matrices. We perform experiments using randomly generated programs and show that partial evaluation has potential for realizing efficient computation in huge scale of programs.

ABSTRACT. ASP programs are a convenient tool for problem solving, whereas with large problem instances the size of the state space can be prohibitive. We consider abstraction as a means of over-approximation and introduce a method to automatically abstract (possibly non-ground) ASP programs that preserves their structure, while reducing the size of the problem. One particular application case is the problem of defining declarative policies for reactive agents and reasoning about them, which we illustrate on examples.

ABSTRACT. Datalog has become a popular language for writing static analyses. Because Datalog is very limited, some implementations of Datalog for static analysis have extended it with new language features. However, even with these features it is hard or impossible to express a large class of analyses because they use logical formulae to represent program state. FormuLog fills this gap by extending Datalog to represent, manipulate, and reason about logical formulae. We have used FormuLog to implement declarative versions of symbolic execution and abstract model checking, analyses previously out of the scope of Datalog-based languages. While this paper focuses on the design of FormuLog and one of the analyses we have implemented in it, it also touches on a prototype implementation of the language and identifies performance optimizations that we believe will be necessary to scale FormuLog to real-world static analysis problems.

ABSTRACT. We study syntactic conditions which guarantee when a CR-Prolog (Consistency Restoring Prolog) program has antichain property: no answer set is a proper subset of another. A notable such condition is that the program's dependency graph being acyclic and having no directed path from one cr-rule head literal to another.