The Beth definability property, a well-known property from classical logic, is investigated in the context of description logics (DLs): if a general L-TBox implicitly defines an L-concept in terms of a given signature, where L is a DL, then does there always exist over this signature an explicit definition in L for the concept? This property has been studied before and used to optimize reasoning in DLs. In this paper a complete classification of Beth definability is provided for extensions of the basic DL ALC with transitive roles, inverse roles, role hierarchies, and/or functionality restrictions, both on arbitrary and on finite structures. Moreover, we present a tableau-based algorithm which computes explicit definitions of at most double exponential size. This algorithm is optimal because it is also shown that the smallest explicit definition of an implicitly defined concept may be double exponentially long in the size of the input TBox. Finally, if explicit definitions are allowed to be expressed in first-order logic then we show how to compute them in EXPTIME.

Many important problems can be compactly represented as quantified boolean formulas (QBF) and solved by general QBF solvers. To date QBF solvers have mainly focused on determining whether or not the input QBF is true or false. However, additional important information about an application can be gathered from its QBF formulation. In this paper we demonstrate that a circuit-based QBF solver can be exploited to obtain a Q-Resolution proof of the truth or the falsity of a QBF. QBFs have a natural interpretation as a two person game and our main result is to show how, via a simple computation, the moves for the winning player can be computed directly from these proofs. This result shows that the proof is a representation of the winning strategy. In previous approaches the winning strategy has often been represented in a way that makes it hard to verify. In our approach the correctness of the strategy follows directly from the correctness of the proof, which is relatively easy to verify.

Log-linear description logics are a family of probabilistic logics integrating various concepts and methods from the areas of knowledge representation and reasoning and statistical relational AI. We define the syntax and semantics of log-linear description logics, describe a convenient representation as sets of first-order formulas, and discuss computational and algorithmic aspects of probabilistic queries in the language. The paper concludes with an experimental evaluation of an implementation of a log-linear DL reasoner.

Fages [1994] introduces the notion of well-supportedness as a key requirement for the semantics of normal logic programs and characterizes the standard answer set semantics in terms of the well-supportedness condition. With the property of well-supportedness, answer sets are guaranteed to be free of circular justifications. In this paper, we extend Fages’ work to description logic programs (or DL-programs). We introduce two forms of well-supportedness for DL-programs. The first one defines weakly well-supported models that are free of circular justifications caused by positive literals in rule bodies. The second one defines strongly well-supported models that are free of circular justifications caused by either positive or negative literals. We then define two new answer set semantics for DL-programs and characterize them in terms of the weakly and strongly well-supported models, respectively. The first semantics is based on an extended Gelfond-Lifschitz transformation and defines weakly well-supported answer sets that are free of circular justifications for the class of DL-programs without negative dl-atoms. The second semantics defines strongly well-supported answer sets which are free of circular justifications for all DL-programs. We show that the existing answer set semantics for DL-programs, such as the weak answer set semantics, the strong answer set semantics, and the FLP-based answer set semantics, satisfy neither the weak nor the strong well-supportedness condition, even for DL-programs without negative dl-atoms. This explains why their answer sets incur circular justifications.

We characterize the expressive power of description logic (DL) TBoxes, both for expressive DLs such as ALC and ALCQIO and lightweight DLs such as DL-Lite and EL. Our characterizations are relative to first-order logic, based on a wide range of semantic notions such as bisimulation, equisimulation, disjoint union, and direct product. We exemplify the use of the characterizations by a first study of the following novel family of decision problems: given a TBox T formulated in one DL, decide whether T can be equivalently rewritten as a TBox in der fragment L' of L.

PODTGolog [Rens, 2010] is a Golog dialect attempting Broadly speaking, my research concerns combining to deal with partially observable MDP (POMDP) logic of action and POMDP theory in a coherent, environments. PODTGolog has not been given a mathematical theoretically sound language for agent programming.

Model checking is one of the most effective techniques in automated system verification. Although this technique can handle complex verifications, model checking tools usually do not give any suggestions on how to repair inconsistent system models. In this paper, we show that approaches developed to update models of Computation Tree Logic (CTL) cannot deal with all kinds of changes. We introduce the concept of CTL model revision: an approach based on belief revision to handle system inconsistency in a static context.

Finally, explore possible methods for decision making in general, have received a lot uses of combinatorial aggregation in sequential voting, of attention in the AI community in recent years. The reasons and discuss theoretical generalisations to more complex logical for this focus are clear: SCT provides tools for the analysis of languages and practical applications. Particularly close to the interests of AI is the to study binary aggregation procedures, inspired by research problem of social choice in combinatorial domains (Chevaleyre in AI. As long as we do not know the intended application of et al., 2008), where the space of alternatives the individuals the model, there is no appropriate set of axioms to concentrate have to choose from has a combinatorial structure. Instead, we prove characterisation results concerning one Definition 1.

A plan with rich control structures like branches and loops can usually serve as a general solution that solves multiple planning instances in a domain. However, the correctness of such generalized plans is non-trivial to define and verify, especially when it comes to whether or not a plan works for all of the infinitely many instances of the problem. In this paper, we give a precise definition of a generalized plan representation called an FSA plan, with its semantics defined in the situation calculus. Based on this, we identify a class of infinite planning problems, which we call one-dimensional (1d), and prove a correctness result that 1d problems can be verified by finite means. We show that this theoretical result leads to an algorithm that does this verification practically, and a planner based on this verification algorithm efficiently generates provably correct plans for 1d problems.

We show how Finite Model Computation (FMC) of first-order theories can efficiently and transparentlybe solved by taking advantage of an extension of Answer Set Programming, called incremental Answer Set Programming (iASP). The idea is to use the incremental parameter in iASP programs to account for the domain size of a model. The FMC problem is then successively addressed for increasing domain sizes until an answer set, representing a finite model of the original first-order theory, is found. We developed a system based on the iASP solver iClingo and demonstrate its competitiveness.