The situation calculus is a popular formalism for reasoning about actions and change. Since the language is first-order, reasoning in the situation calculus is undecidable in general.  An important question then is how to weaken reasoning in a principled way to guarantee decidability. Existing approaches either drastically limit the representation of the action theory or neglect important aspects such as sensing. In this paper we propose a model of limited belief for the epistemic situation calculus, which allows very expressive knowledge bases and handles both physical and sensing actions. The model builds on an existing approach to limited belief in the static case. We show that the resulting form of limited reasoning is sound with respect to the original epistemic situation calculus and eventually complete for a large class of formulas. Moreover, reasoning is decidable.

Belief merging aims at defining the beliefs of a group of agents from the beliefs of each member of the group. It is related to more general notions of aggregation from economics (social choice theory). Two main subclasses of belief merging operators exist: majority operators which are related to utilitarianism, and arbitration operators which are related to egalitarianism. Though utilitarian (majority) operators have been extensively studied so far, there is much less work on egalitarian operators. In order to fill the gap, we investigate possible translations in a belief merging framework of some egalitarian properties and concepts coming from social choice theory, such as Sen-Hammond equity, Pigou- Dalton property, median, and Lorenz curves. We study how these properties interact with the standard rationality conditions considered in belief merging. Among other results, we show that the distance-based merging operators satisfying Sen-Hammond equity are mainly those for which leximax is used as the aggregation function.

Datalog+/- is a conceptually very simple formalism that extends plain Datalog with features such as existential quantifiers, equalities, and the falsum in rule heads and, at the same time, restricts the rule syntax so as to achieve decidability and, when required, tractability. Datalog+/- provides a uniform framework for query answering and reasoning with incomplete data. It generalizes disparate other KR formalisms such as plain Datalog, description logics (DLs), in particular, DL-Lite and EL, F-Logic Lite, highly relevant fragments of UML class diagrams, data-exchange formalisms, graph query languages such as SPARQL, and so on. The goal of this paper is to give concise answers to frequently asked questions about Datalog+/-.

The standard way of answering queries over incomplete databases is to compute certain answers, defined as the intersection of query answers on all complete databases that the incomplete database represents. But is this universally accepted definition correct? We argue that this "one-size-fits-all" definition can often lead to counterintuitive or just plain wrong results, and propose an alternative framework for defining certain answers. The idea of the framework is to move away from the standard, in the database literature, assumption that query results be given in the form of a database object, and to allow instead two alternative representations of answers: as objects defining all other answers, or as knowledge we can deduce with certainty about all such answers. We show that the latter is often easier to achieve than the former, that in general certain answers need not be defined as intersection, and may well contain missing information in them. We also show that with a proper choice of semantics, we can often reduce computing certain answers - as either objects or knowledge - to standard query evaluation. We describe the framework in the most general way, applicable to a variety of data models, and test it on three concrete relational semantics of incompleteness: open, closed, and weak closed world.

The Region Connection Calculus (RCC) is a well-known calculus for representing part-whole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The computational complexity of reasoning with RCC has been investigated in depth in the literature. Most of these works focus on the consistency of RCC constraint networks. In this paper, we consider the important problem of redundant RCC constraints. For a set Γ of RCC constraints, we say a constraint (x R y) in Γ is redundant if it can be entailed by the rest of Γ. A prime network of Γ is a subset of Γ which contains no redundant constraints but has the same solution set as Γ. It is natural to ask how to compute a prime network, and when it is unique. In this paper, we show that this problem is in general co-NP hard, but becomes tractable if Γ is over a tractable subclass of RCC. If S is a tractable subclass in which weak composition distributes over non-empty intersections, then we can show that Γ has a unique prime network, which is obtained by removing all redundant constraints from Γ. As a byproduct, we identify a sufficient condition for a path-consistent network being minimal.

Input languages of answer set solvers are based on the mathematically simple concept of a stable model. But many useful constructs available in these languages, including local variables, conditional literals, and aggregates, cannot be easily explained in terms of stable models in the sense of the original definition of this concept and its straightforward generalizations. Manuals written by designers of answer set solvers usually explain such constructs using examples and informal comments that appeal to the user’s intuition, without references to any precise semantics. We propose to approach the problem of defining the semantics of Gringo programs by translating them into the language of infinitary propositional formulas. This semantics allows us to study equivalent transformations of Gringo programs using natural deduction in infinitary propositional logic, so that the properties of these programs can be more precisely characterized. In this way, we aim to create a foundation on which important issues such as the correctness of GRINGO programs and optimization methods may be more formally studied.

Logic programs with ordered disjunction (LPODs) (Brewka 2002) generalize normal logic programs by combining alternative and ranked options in the heads of rules. It has been showed that LPODs are useful in a number of areas including game theory, policy languages, planning and argumentations. In this paper, we extend propositional LPODs to the first-order case, where a classical second-order formula is defined to capture the stable model semantics of the underlying first-order LPODs. We then develop a progression semantics that is equivalent to the stable model semantics but naturally represents the reasoning procedure of LPODs. We show that on finite structures, every LPOD can be translated to a first order sentence, which provides a basis for computing stable models of LPODs. We further study the complexity and expressiveness of LPODs and prove that almost positive LPODs precisely capture first-order normal logic programs, which indicates that ordered disjunction itself and constraints are sufficient to represent negation as failure.

This paper presents a meta-algorithm for the computation of preferred labellings, based on the general recursive schema for argumentation semantics called SCC-Recursiveness. The idea is to recursively decompose a framework so as to compute semantics labellings on restricted sub-frameworks, in order to reduce the computational effort. The meta-algorithm can be instantiated with a specific "base algorithm", applied to the base case of the recursion, which can be obtained by generalizing existing algorithms in order to compute labellings in restricted sub-frameworks. We devise for this purpose a generalization of a SAT-based algorithm, and provide an empirical investigation to show the significant improvement of performances obtained by exploiting the SCC-recursive schema.

Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at the second level of the Polynomial Hierarchy or even higher, and hence polynomial-time transformations to SAT are not possible, unless the hierarchy collapses. Recent research shows that in certain cases one can break through these complexity barriers by fixed-parameter tractable (fpt) reductions which exploit structural aspects of problem instances in terms of problem parameters. In this paper we develop a general theoretical framework that supports the classification of parameterized problems on whether they admit such an fpt-reduction to SAT or not. We instantiate our theory by classifying the complexities of several case study problems, with respect to various natural parameters. These case studies include the consistency problem for disjunctive answer set programming and a robust version of constraint satisfaction.

The study of extension-based semantics within the seminal abstract argumentation model of Dung has largely focused on definitional, algorithmic and complexity issues. In contrast, matters relating to comparisons of representational limits, in particular, the extent to which given collections of extensions are expressible within the formalism, have been under-developed. As such, little is known concerning conditions under which a candidate set of subsets of arguments are “realistic” in the sense that they correspond to the extensions of some argumentation framework AF for a semantics of interest. In this paper we present a formal basis for examining extension-based semantics in terms of the sets of extensions that these may express within a single AF. We provide a number of characterization theorems which guarantee the existence of AFs whose set of extensions satisfy specific conditions and derive preliminary complexity results for decision problems that require such characterizations.