First-order disjunctive logic programming vs normal logic programming

In this paper, we study the expressive power of firstorder disjunctive logic programming (DLP) and normal logic programming (NLP) under the stable model semantics. We show that, unlike the propositional case, first-order DLP is strictly more expressive than NLP. This result still holds even if auxiliary predicates are allowed, assuming NP ≠ coNP. On the other side, we propose a partial translation from first-order DLP to NLP via unfolding and shifting, which suggests a sound yet incomplete approach to implement DLP via NLP solvers. We also identify some NLP definable subclasses, and conjecture to exactly capture NLP definability by unfolding and shifting

From disjunctive to normal logic programs via unfolding and shifting

We show that every propositional disjunctive logic program under the answer set semantics can be equivalently transformed into a normal one via unfolding and shifting. More precisely, after iteratively applying the unfolding operator for some rules in a disjunctive program, its shifted program, which is a normal program, must have the same answer sets as the original disjunctive program

First-order default logic revisited

Reiter’s original proposal for default logic is unsatisfactory for open default theories because of Skolemization and grounding. In this paper, we reconsider this long-standing problem and propose a new world view semantics for first-order default logic. Roughly speaking, a world view of a first-order default theory is a maximal collection of structures satisfying the default theory where the default part is fixed by the world view itself. We show how this semantics generalizes classical first-order logic and first-order answer set programming, and we discuss its connections to Reiter’s semantics and other related semantics. We also argue that first-order default logic under the world view semantics provides a rich framework for integrating classical logic based and rule based formalisms in the first-order case

RDL : enhancing description logic with rules

In this paper, we propose Rule Description Logic (RDL) for enhancing Description Logic (DL) with nonmonotonic recursive rules, like those in Answer Set Programming (ASP). We define the world view semantics for RDL and show that it is faithful with respect to both DL and ASP. More importantly, we show that the full language of RDL is decidable

On the progression semantics and boundedness of answer set programs

In this paper, we propose a progression semantics for first-order answer set programs. Based on this new semantics, we are able to define the notion of boundedness for answer set programming. We prove that boundedness coincides with the notions of recursion-free and loop-free under program equivalence, and is also equivalent to first-order definability of answer set programs on arbitrary structures

A logical study of partial entailment

We introduce a novel logical notion-partial entailment-to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set Γ intuitively means that under the circumstance of Γ, if P is true then some “part" of Q will also be true. We distinguish three different kinds of partial entailments and formalize them by using an extended notion of prime implicant. We study their semantic properties, which show that, surprisingly, partial entailments fail for many simple inference rules. Then, we study the related computational properties, which indicate that partial entailments are relatively diffcult to be computed. Finally, we consider a potential application of partial entailments in reasoning about rational agents

Forgetting revisited

In this paper, we propose an alternative notion, called weak forgetting, of forgetting a set of predicates in a first-order theory. One important feature of this new notion is that the result of weak forgetting is always first-order expressible. In contrast, this is not the case for the traditional notion of forgetting, called strong forgetting, introduced by Lin and Reiter. As a consequence, these two notions are not exactly the same. Interestingly, we prove that they coincide when the result of strong forgetting is first-order expressible. We also present a representation theorem to characterize weak forgetting from different aspects

Progression semantics for disjunctive logic programs

In this paper, we extend the progression semantics for first-order disjunctive logic programs and show that it coincides with the stable model semantics. Based on it, we further show how disjunctive answer set programming is related to Satisfiability Modulo Theories

A progression semantics for first-order logic programs

In this paper, we propose a progression semantics for first-order normal logic programs, and show that it is equivalent to the well-known stable model (answer set) semantics. The progressional definition sheds new insights into Answer Set Programming (ASP), for instance, its relationships to Datalog, First-Order Logic (FOL) and Satisfiability Modulo Theories (SMT). As an example, we extend the notion of boundedness in Datalog for ASP, and show that it coincides with the notions of recursion-freeness and loop-freeness under program equivalence. In addition, we prove that boundedness precisely captures first-order definability for normal logic programs on arbitrary structures. Finally, we show that the progressional definition suggests an alternative translation from ASP to SMT, which yields a new way of implementing first-order ASP

Modeling abstract behavior : a dynamic logic approach

Modeling abstract behavior is essential for intelligent agents under incomplete and uncertain environments. In this paper, we extend Propositional Dynamic Logic (PDL) to Propositional Abstract Dynamic Logic (PADL) for modeling abstract behavior in two aspects. On the one hand, we treat the task of finding a plan to achieve a certain formula as an abstract action. On the other hand, we explicitly represent the subsumption relation between two actions as a formula in the language. We propose the semantics for the two operators and discuss some important related properties