The Sentential Decision Diagram (SDD) is a recently proposed representation of Boolean functions, containing Ordered Binary Decision Diagrams (OBDDs) as a distinguished subclass. While OBDDs are characterized by total variable orders, SDDs are characterized by dissections of variable orders, known as vtrees. Despite this generality, SDDs retain a number of properties, such as canonicity and a polytime apply operator, that have been critical to the practical success of OBDDs. Moreover, upper bounds on the size of SDDs were also given, which are tighter than comparable upper bounds on the size of OBDDs. In this paper, we analyze more closely some of the theoretical properties of SDDs and their size. In particular, we consider the impact of basing decisions on sentences (using dissections as in SDDs), in comparison to basing decisions on variables (using total variable orders as in OBDDs). Here, we identify a class of Boolean functions where basing decisions on sentences using dissections of a variable order can lead to exponentially more compact SDDs, compared to OBDDs based on the same variable order. Moreover, we identify a fundamental property of the decompositions that underlie SDDs and use it to show how certain changes to a vtree can also lead to exponential differences in the size of an SDD.

Logic programs with abstract constraint atoms proposed by Marek and Truszczynski are very general logic programs.They are general enough to captureaggregate logic programs as well asrecently proposed description logic programs.In this paper, we propose a well-founded semantics for basic logic programs with arbitrary abstract constraint atoms, which are sets of rules whose heads have exactly one atom. Weshow that similar to the well-founded semanticsof normal logic programs, it has many desirable properties such as that it can becomputed in polynomial time, and is always correct with respect to theanswer set semantics. This paves the way for using our well-founded semanticsto simplify these logic programs. We also show how our semantics can be applied toaggregate logic programs and description logic programs, and compare itto the well-founded semantics already proposed for these logic programs.

The FLP semantics presented by (Faber, Leone, and Pfeifer 2004) has been widely used to define answer sets, called FLP answer sets, for different types of logic programs such as logic programs with aggregates, description logic programs (dl-programs), Hex programs, and logic programs with first-order formulas (general logic programs). However, it was recently observed that the FLP semantics may produce unintuitive answer sets with circular justifications caused by self-supporting loops. In this paper, we address the circular justification problem for general logic programs by enhancing the FLP semantics with a level mapping formalism. In particular, we extend the Gelfond-Lifschitz three step definition of the standard answer set semantics from normal logic programs to general logic programs and define for general logic programs the first FLP semantics that is free of circular justifications. We call this FLP semantics the well-justified FLP semantics. This method naturally extends to general logic programs with additional constraints like aggregates, thus providing a unifying framework for defining the well-justified FLP semantics for various types of logic programs. When this method is applied to normal logic programs with aggregates, the well-justified FLP semantics agrees with the conditional satisfaction based semantics defined by (Son, Pontelli, and Tu 2007); and when applied to dl-programs, the semantics agrees with the strongly well-supported semantics defined by (Shen 2011).

Temporal Action Logics (TAL) is a class of temporal logics for reasoning about actions. We present a reformulation of TAL in Answer Set Programming (ASP), and discuss some synergies it brings. First, the reformulation provides a means to compute TAL using efficient answer set solvers. Second, TAL provides a structured high-level language for ASP (possibly with constraint solving). Third, the reformulation allows us to compute integration of TAL and ontologies using answer set solvers, and we illustrate its usefulness in the healthcare domain in the context of medical expert systems.

The paper identifies a special case in which the complex problem of synthesis from specifications in temporal-epistemic logic can be reduced to the simpler problem of model checking such specifications. An application is given of strategy synthesis in pursuit-evasion games, where one or more pursuers with incomplete information aim to discover theexistence of an evader. Experimental results are provided to evaluate the feasibility of the approach.

Abduction belongs to the most fundamental reasoning methods. It is a method for reverse inference, this means one is interested in explaining observed behavior by finding appropriate causes. We study logic-based abduction, where knowledge is represented by propositional formulas. The computational complexity of this problem is highly intractable in many interesting settings. In this work we therefore present an extensive parameterized complexity analysis of abduction within various fragments of propositional logic together with (combinations of) natural parameters.

Query answering over Description Logic (DL) ontologies has become a vibrant field of research. Efficient realizations often exploit database technology and rewrite a given query to an equivalent SQL or Datalog query over a database associated with the ontology. This approach has been intensively studied for conjunctive query answering in the DL-Lite and EL families, but is much less explored for more expressive DLs and queries. We present a rewriting-based algorithm for conjunctive query answering over Horn-SHIQ ontologies, possibly extended with recursive rules under limited recursion as in DL+log. This setting not only subsumes both DL-Lite and EL, but also yields an algorithm for answering (limited) recursive queries over Horn-SHIQ ontologies (an undecidable problem for full recursive queries). A prototype implementation shows its potential for applications, as experiments exhibit efficient query answering over full Horn-SHIQ ontologies and benign downscaling to DL-Lite, where it is competitive with comparable state of the art systems.

Given a partially observable dynamic system and a diagnoser observing its evolution over time, diagnosability analysis formally verifies (at design time) if the diagnosis system will be able to infer (at runtime) the required information on the hidden part of the dynamic state. Diagnosability directly depends on the availability of observations, and can be guaranteed by different sets of sensors, possibly associated with different costs. In this paper, we tackle the problem of synthesizing observability requirements, i.e. automatically discovering a set of observations that is sufficient to guarantee diagnosability. We propose a novel approach with the following characterizing features. First, it fully covers a comprehensive formal framework for diagnosability analysis, and enables ranking configurations of observables in terms of cost, minimality, and diagnosability delay. Second, we propose two complementary algorithms for the synthesis of observables. Third, we describe an efficient implementation that takes full advantage of mature symbolic model checking techniques. The proposed approach is thoroughly evaluated over a comprehensive suite of benchmarks taken from the aerospace domain.

Recently a logic programming language AC was proposed by Mellarkod et al. (2008) to integrate answer set programming (ASP) and constraint logic programming. Similarly, Gebser et al. (2009) proposed a CLINGCON language integrating ASP and finite domain constraints. These languages allow new efficient inference algorithms that combine traditional ASP procedures and other methods in constraint programming. In this paper we show that a transition system introduced by Nieuwenhuis et al. (2006) to model SAT solvers can be extended to model the "hybrid" Acsolver algorithm by Mellarkod et al. developed for simple AC programs and the Clingcon algorithm by Gebser et al. for clingcon programs. We define weakly-simple programs and show how the introduced transition systems generalize the Acsolver and Clingcon algorithms to such programs. Finally, we state the precise relation between AC and CLINGCON languages and the Acsolver and Clingcon algorithms.

The behavior composition problem involves automatically building a controller that is able to realize a desired, but unavailable, target system (e.g., a house surveillance) by suitably coordinating a set of available components (e.g., video cameras, blinds, lamps, a vacuum cleaner, phones, etc.) Previous work has almost exclusively aimed at bringing about the desired component in its totality, which is highly unsatisfactory for unsolvable problems. In this work, we develop an approach for approximate behavior composition without departing from the classical setting, thus making the problem applicable to a much wider range of cases. Based on the notion of simulation, we characterize what a maximal controller and the "closest" implementable target module (optimal approximation) are, and show how these can be computed using ATL model checking technology for a special case. We show the uniqueness of optimal approximations, and prove their soundness and completeness with respect to their imported controllers.