We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point characterization, investigate closure properties of model classes, present an axiomatization and prove its completeness, and investigate alternative axiomatizations and normalized proofs. We investigate decidability and complexity issues of the logic and prove that the entailment problem is NP-hard and belongs to EXPSPACE. We show that by restricting to predictive formulas, the entailment problem is decidable in pseudo-linear time.

Multi-context Systems (MCSs) are a formalism for systems consisting of knowledge bases (possibly heterogeneous and non-monotonic) that are interlinked via bridge rules, where the global system semantics emerges from the local semantics of the knowledge bases (also called contexts) in an equilibrium. While MCSs and related formalisms are inherently targeted for distributed set- tings, no truly distributed algorithms for their evaluation were available. We address this short- coming and present a suite of such algorithms which includes a basic algorithm DMCS, an ad- vanced version DMCSOPT that exploits topology-based optimizations, and a streaming algorithm DMCS-STREAMING that computes equilibria in packages of bounded size. The algorithms be- have quite differently in several respects, as experienced in thorough experimental evaluation of a system prototype. From the experimental results, we derive a guideline for choosing the appropriate algorithm and running mode in particular situations, determined by the parameter settings.

To date, work on formalizing connectionist computation in a way that is at least Turing-complete has focused on recurrent architectures and developed equivalences to Turing machines or similar super-Turing models, which are of more theoretical than practical significance. We instead develop connectionist computation within the framework of information propagation networks extended with unbounded recursion, which is related to constraint logic programming and is more declarative than the semantics typically used in practical programming, but is still formally known to be Turing-complete. This approach yields contributions to the theory and practice of both connectionist computation and programming languages. Connectionist computations are carried out in a way that lets them communicate with, and be understood and interrogated directly in terms of the high-level semantics of a general-purpose programming language. Meanwhile, difficult (unbounded-dimension, NP-hard) search problems in programming that have previously been left to the programmer to solve in a heuristic, domain-specific way are solved uniformly a priori in a way that approximately achieves information-theoretic limits on performance.

This paper describes a modular action language, ALM, dedicated to the specification of complex dynamic systems. One of the main goals of the language is to facilitate the development and testing of knowledge representation libraries. We present the implementation of a large scale library of commonsense concepts, achieved by porting knowledge from the Component Library (CLIB) into ALM. Our choice of CLIB as a source of inspiration is justified by the well-founded methodology used by its authors in selecting the general concepts it contains, and its extensive testing in the context of the Automated User-centered Reasoning and Acquisition System. The resulting ALM library has the additional advantage of incorporating established knowledge representation methodologies developed in the action language research community.

This paper proposes an integration of the situation calculus with justification logic. Justification logic can be seen as a refinement of a modal logic of knowledge and belief to one in which knowledge not only is something that holds in all possible worlds, but also is justified. The work is an extension of that of Scherl and Levesque's integration of the situation calculus with a modal logic of knowledge. We show that the solution developed here retains all of the desirable properties of the earlier solution while incorporating the enhanced expressibility of having justifications.

We present a probabilistic extension of logic programs under the stable model semantics, inspired by the idea of Markov Logic Networks. The proposed language, called LP MLN , is a generalization of logic programs under the stable model semantics, and as such, embraces the rich body of research in knowledge representation. The language is also a generalization of ProbLog, and is closely related to Markov Logic Networks, which implies that the computation can be carried out by the techniques developed for them.  LP MLN appears to be a natural language for probabilistic answer set programming, and as an example we show how an elaboration tolerant representation of transition systems in answer set programs can be naturally extended to the probabilistic setting.

This paper is concerned with knowledge compilation (KC), a family of approaches developed in AI for more than twenty years. Knowledge compilation consists in pre-processing some pieces of the available information in order to improve the computational efficiency (especially, the time complexity) of some tasks. In this paper, the focus is laid on three KC topics which gave rise to many works: the development of knowledge compilation techniques for the clausal entailment problem in propositional logic, the concept of compilability and the notion of knowledge compilation map. The three topics, as well as an overview of the main results from the literature, are presented. Some recent research lines are also discussed.

Many computer science problems can be naturally and compactly expressed using quantified Boolean formulas (QBFs). Evaluating thetruth or falsity of a QBF is an important task, and constructing the corresponding model or countermodel can be as important and sometimes even more useful in practice. Modern search and learning based QBF solvers rely fundamentally on resolution and can be instrumented to produce resolution proofs, from which in turn Skolem-function models and Herbrand-function countermodels can be extracted. These (counter)models are the key enabler of various applications. Not until recently the superiority of long-distanceresolution (LQ-resolution) to short-distance resolution(Q-resolution) was demonstrated. While a polynomial algorithm exists for (counter)model extraction from Q-resolution proofs, it remains open whether it exists forLQ-resolution proofs. This paper settles this open problem affirmatively by constructing a linear-time extraction procedure. Experimental results show the distinct benefits of the proposed method in extracting high quality certificates from some LQ-resolution proofs that are not obtainable from Q-resolution proofs.

This paper proposes an alternative definition of elementary loops and extends the notion of proper loops for disjunctive logic programs. Different from normal logic programs, the computational complexities of recognizing elementary loops and proper loops for disjunctive programs are coNP-complete. To address this problem, we introduce weaker versions of both elementary loops and proper loops and provide polynomial time algorithms for identifying them respectively. On the other hand, based on the notion of elementary loops, the class of Head-Elementary-loop-Free (HEF) programs was presented, which can be turned into equivalent normal logic programs by shifting head atoms into bodies. However, the problem of recognizing an HEF program is coNP-complete. Then we present a subclass of HEF programs which generalizes the class of Head-Cycle-Free programs and provide a polynomial time algorithm to identify them. At last, some experiments show that both elementary loops and proper loops could be replaced by their weak versions in practice.

In this paper we describe asprin, a general, flexible, and extensible framework for handling preferences among the stable models of a logic program. We show how complex preference relations can be specified through user-defined preference types and their arguments. We describe how preference specifications are handled internally by so-called preference programs, which are used for dominance testing. We also give algorithms for computing one, or all, optimal stable models of a logic program. Notably, our algorithms depend on the complexity of the dominance tests and make use of multi-shot answer set solving technology.