System f2lp – computing answer sets of first-order formulas

Abstract. We present an implementation of the general language of stable models proposed by Ferraris, Lee and Lifschitz. Under certain conditions, system f2lp turns a first-order theory under the stable model semantics into an answer set program, so that existing answer set solvers can be used for computing the general language. Quantifiers are first eliminated and then the resulting quantifier-free formulas are turned into rules. Based on the relationship between stable models and circumscription, f2lp can also serve as a reasoning engine for general circumscriptive theories. We illustrate how to use f2lp to compute the circumscriptive event calculus.

Representing First-Order Causal Theories by Logic Programs

Nonmonotonic causal logic, introduced by Norman McCain and Hudson Turner, became a basis for the semantics of several expressive action languages. McCain's embedding of definite propositional causal theories into logic programming paved the way to the use of answer set solvers for answering queries about actions described in such languages. In this paper we extend this embedding to nondefinite theories and to first-order causal logic.Comment: 29 pages. To appear in Theory and Practice of Logic Programming (TPLP); Theory and Practice of Logic Programming, May, 201

System aspmt2smt: Computing ASPMT Theories by SMT Solvers

Abstract. Answer Set Programming Modulo Theories (ASPMT) is an approach to combining answer set programming and satisfiability modulo theories based on the functional stable model semantics. It is shown that the tight fragment of ASPMT programs can be turned into SMT instances, thereby allowing SMT solvers to compute stable models of ASPMT programs. In this paper we present a compiler called ASPSMT2SMT, which implements this translation. The system uses ASP grounder GRINGO and SMT solver Z3. GRINGO partially grounds input programs while leaving some variables to be processed by Z3. We demonstrate that the system can effectively handle real number computations for reasoning about continuous changes.

On the Relationships Among Probabilistic Extensions of Answer Set Semantics

abstract: Answer Set Programming (ASP) is one of the main formalisms in Knowledge Representation (KR) that is being widely applied in a large number of applications. While ASP is effective on Boolean decision problems, it has difficulty in expressing quantitative uncertainty and probability in a natural way. Logic Programs under the answer set semantics and Markov Logic Network (LPMLN) is a recent extension of answer set programs to overcome the limitation of the deterministic nature of ASP by adopting the log-linear weight scheme of Markov Logic. This thesis investigates the relationships between LPMLN and two other extensions of ASP: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. The studied relationships show how different extensions of answer set programs are related to each other, and how they are related to formalisms in Statistical Relational Learning, such as Problog and MLN, which have shown to be closely related to LPMLN. The studied relationships compare the properties of the involved languages and provide ways to compute one language using an implementation of another language. This thesis first presents a translation of LPMLN into programs with weak constraints. The translation allows for computing the most probable stable models (i.e., MAP estimates) or probability distribution in LPMLN programs using standard ASP solvers so that the well-developed techniques in ASP can be utilized. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl’s Causal Models, that are shown to be translatable into LPMLN. This thesis also presents a translation of P-log into LPMLN. The translation tells how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers or MLN solvers.Dissertation/ThesisMasters Thesis Computer Science 201

Representing Hybrid Transition Systems in an Action Language Modulo ODEs

abstract: Several physical systems exist in the real world that involve continuous as well as discrete changes. These range from natural dynamic systems like the system of a bouncing ball to robotic dynamic systems such as planning the motion of a robot across obstacles. The key aspects of effectively describing such dynamic systems is to be able to plan and verify the evolution of the continuous components of the system while simultaneously maintaining critical constraints. Developing a framework that can effectively represent and find solutions to such physical systems prove to be highly advantageous. Both hybrid automata and action languages are formal models for describing the evolution of dynamic systems. The action language C+ is a rich and expressive language framework to formalize physical systems, but can be used only with physical systems in the discrete domain and is limited in its support of continuous domain components of such systems. Hybrid Automata is a well established formalism used to represent such complex physical systems at a theoretical level, however it is not expressive enough to capture the complex relations between the components of the system the way C+ does. This thesis will focus on establishing a formal relationship between these two formalisms by showing how to succinctly represent Hybrid Automata in an action language which in turn is defined as a high-level notation for answer set programming modulo theories (ASPMT) --- an extension of answer set programs in the first-order level. Furthermore, this encoding framework is shown to be more effective and expressive than Hybrid Automata by highlighting its ability in allowing states of a hybrid transition system to be defined by complex relations among components that would otherwise be abstracted away in Hybrid Automata. The framework is further realized in the implementation of the system CPLUS2ASPMT, which takes advantage of state of the art ODE(Ordinary Differential Equations) based SMT solver dReal to provide support for ODE based evolution of continuous components of a dynamic system.Dissertation/ThesisMasters Thesis Computer Science 201

Representing First-Order Causal Theories by Logic Programs

Nonmonotonic causal logic, introduced by McCain and Turner (McCain, N. and Turner, H. 1997. Causal theories of action and change. In Proceedings of National Conference on Artificial Intelligence (AAAI), Stanford, CA, 460–465) became the basis for the semantics of several expressive action languages. McCain\u27s embedding of definite propositional causal theories into logic programming paved the way to the use of answer set solvers for answering queries about actions described in such languages. In this paper we extend this embedding to nondefinite theories and to the first-order causal logic