We study a logical system FQHT that is appropriate for reasoning about nonmonotonic theories with intensional functions as treated in the approach of Bartholomew and Lee (2012). We provide a logical semantics, a Gentzen style proof theory and establish completeness results. The adequacy of the approach is demonstrated by showing that it captures the Bartholemew/Lee semantics and satisfies a strong equivalence property.

Existing languages in the valued decision diagrams (VDDs) family, including ADD, AADD, and those of the SLDD family, prove to be valuable target languages for compiling multivariate functions. However, their efficiency is directly related to the size of the compiled formulae.In practice, the existence of canonical forms may have a major impact on the size of the compiled VDDs. While efficient normalization procedures have been pointed out for ADD and AADD, the canonicity issue for SLDD formulae has not been addressed so far. In this paper, the SLDD family is revisited. We modify the algebraic requirements imposed on the valuation structure so as to ensure tractable conditioning, optimization and normalization for some languages of the revisited SLDD family. We show that AADD is captured by this family. Finally, we compare the spatial efficiency of some languages of this family, from both the theoretical side and the practical side.

The knowledge compilation map introduced by Darwiche and Marquis takes advantage of a number of concepts (mainly queries, transformations, expressiveness, and succinctness) to compare the relative adequacy of representation languages to some AI problems. However, the framework is limited to the comparison of languages that are interpreted in a homogeneous way (formulae are interpreted as Boolean functions). This prevents one from comparing, on a formal basis, languages that are close in essence, such as OBDD, MDD, and ADD. To fill the gap, we present a generalized framework into which comparing formally heterogeneous representation languages becomes feasible. In particular, we explain how the key notions of queries and transformations, expressiveness, and succinctness can be lifted to the generalized setting.

Nonmonotonic Description Logic (DL) programs support rule-based reasoning on top of Description Logic ontologies, using a well-defined query interface. However, the interaction of the rules and the ontology may cause inconsistency such that no answer set (i.e. model) exists. We thus consider repairing DL-programs, i.e., changing formulas to obtain consistency. Viewing the data part of the ontology as the source of inconsistency, we define program repairs and repair answer sets based on changes to it. We analyze the complexity of the notion, and we extend an algorithm for evaluating DL-programs to compute repair answer sets, under optional selection of preferred repairs. The extension involves a generalized ontology repair problem, in which the entailment and non-entailment of sets of queries with updates to the ontology must be achieved. While this is intractable in general, we identify for the Description Logic DL-Lite_A some tractable classes of preferred repairs that are useful in practice.

We define the class of e-bounded theories in the epistemic situation calculus, where the number of fluent atoms that the agent thinks may be true is bounded by a constant. Such theories can still have an infinite domain and an infinite set of states. We show that for them verification of an expressive class of first-order mu-calculus temporal epistemic properties is decidable. We also show that if the agent’s knowledge in the initial situation is e-bounded and the objective part of an action theory maintains boundedness, then the entire epistemic theory is e-bounded.

We present a new approach to token-level causal reasoning that we call Sequences Of Mechanisms (SoMs), which models causality as a dynamic sequence of active mechanisms that chain together to propagate causal influence through time. We motivate this approach by using examples from AI and robotics and show why existing approaches are inadequate. We present an algorithm for causal reasoning based on SoMs, which takes as input a knowledge base of first-order mechanisms and a set of observations, and it hypothesizes which mechanisms are active at what time. We show empirically that our algorithm produces plausible causal explanations of simulated observations generated from a causal model. We argue that the SoMs approach is qualitatively closer to the human causal reasoning process, for example, it will only include relevant variables in explanations. We present new insights about causal reasoning that become apparent with this view. One such insight is that observation and manipulation do not commute in causal models, a fact which we show to be a generalization of the Equilibration-Manipulation Commutability of [Dash(2005)].

Rewriting-based approaches for answering queries over an OWL 2 DL ontology have so far been developed mainly for Horn fragments of OWL 2 DL. In this paper, we study the possibilities of answering queries over non-Horn ontologies using datalog rewritings. We prove that this is impossible in general even for very simple ontology languages, and even if PTIME = NP. Furthermore, we present a resolution-based procedure for SHI ontologies that, in case it terminates, produces a datalog rewriting of the ontology. We also show that our procedure necessarily terminates on DL-Lite Bool H,+ ontologies — an extension of OWL 2 QL with transitive roles and Boolean connectives.

Wastl introduced for first time a tableaux-like method based on an inference system for deriving all minimal keys from a relational schema. He introduced two inference rules and built an automated method over them.In this work we tackle the key finding problem with a tableaux method, but we will use two inference rules inspired by the Simplification Logic for Functional Dependencies. Wastl's method requires the input to be a set of functional dependencies with atomic right hand sides. Therefore, it is necessary to apply fragmentation rule with the consequent increasing of the input.The main novelty of our rules is that they deal with generalized formulas, avoiding the fragmentation needed in the former tableaux. Finally we illustrate the advantages of our new tableaux method with an experiment.

Description Logic Knowledge and Action Bases (KABs) have been recently introduced as a mechanism that provides a semantically rich representation of the information on the domain of interest in terms of a DL KB and a set of actions to change such information over time, possibly introducing new objects. In this setting, decidability of verification of sophisticated temporal properties over KABs, expressed in a variant of first-order mu-calculus, has been shown. However, the established framework treats inconsistency in a simplistic way, by rejecting inconsistent states produced through action execution. We address this problem by showing how inconsistency handling based on the notion of repairs can be integrated into KABs, resorting to inconsistency-tolerant semantics. In this setting, we establish decidability and complexity of verification.

We present various new concepts and results related to abstract dialectical frameworks (ADFs), a powerful generalization of Dung's argumentation frameworks (AFs). In particular, we show how the existing definitions of stable and preferred semantics which are restricted to the subcase of so-called bipolar ADFs can be improved and generalized to arbitrary frameworks. Furthermore, we introduce preference handling methods for ADFs, allowing for both reasoning with and about preferences. Finally, we present an implementation based on an encoding in answer set programming.