This is also a key issue in formalizing deals with incomplete information, preferences, negotiation, which seems to prefer argumentationbased and changing goals. We assume that each negotiation [Rahwan et al., 2003]. Recent proposals agent is equipped with a knowledge base for negotiation on formalizing negotiation (see, e.g., [Amgoud et al., 2006; which consists of a CRprogram, a set of possible Kakas and Moraitis, 2006; Rahwan et al., 2003]) seem to be assumptions, and a set of ordered goals.

Current Answer Set Programming (ASP) solvers largely build on Datalog, which, unlike general logic programming, lacks function symbols. This limitation makes ASP decidable, but greatly complicates the modeling of indefinite time, recursive data structures (e.g., lists), and infinite processes and objects in general. Recent research thus aims at finding decidable fragments of ASP with function symbols and studying their complexity. We identify bidirectional ASP programs as an expressive, but yet decidable, language that is useful, e.g., for reasoning about actions involving both the future and the past. We tightly characterize the computational complexity of bidirectional programs and some of their subclasses, addressing the main reasoning tasks. Our results also show that the recently introduced FDNC programs can be extended by inverse rules while retaining decidability, but computational costs are unavoidably higher.

We address the problem of providing a logical formalization of arithmetic in declarative modelling languages for NP search problems. The challenge is to simultaneously allow quantification over an infinite domain such as the natural numbers, provide natural modelling facilities, and control expressive power of the language. To address the problem, we introduce an extension of the model expansion (MX) based framework to finite structures embedded in an infinite secondary structure, together with "double-guarded" logics for representing MX specifications for these structures. The logics also contain multi-set functions (aggregate operations). Our main result is that these logics capture the complexity class NP on "small-cost" arithmetical structures. 

We consider query answering on Description Logic (DL) ontologies with DBoxes, where a DBox is a set of assertions on individuals involving atomic concepts and roles called DBox predicates. The extension of a DBox predicate is exactly defined in every interpretation by the contents of the DBox, i.e., a DBox faithfully represents a database whose table names are the DBox predicates and the tuples are the DBox assertions. Our goals are (i) to find out whether the answers to a given query are solely determined by the DBox predicates and, if so, (ii) to find a rewriting of the query in terms of them. The resulting query can then be efficiently evaluated using standard database technology. We have that (i) can be reduced to entailment checking and (ii) can be reduced to finding an interpolant. We present a procedure for computing interpolants in the DL ALC with general TBoxes. We extend the procedure with standard tableau optimisations, and we discuss abduction as a technique for amending ontologies to gain definability of queries of interest.

We consider all possible games that have unique PNE payoffs. Our starting point is the classes of games that can be expressed by a conjunction class of two-person strictly competitive games. We first formulate of two binary clauses, and our program rediscovered the notions of games, strictly competitive games and Kats and Thisse's class of weakly unilaterally PNEs in first-order logic. Under our formulation, a class of competitive two-person games, and came games corresponds to a first-order sentence. In particular, the up with several other classes of games that have sentence that corresponds to the class of strictly competitive unique pure Nash equilibrium payoffs. It also came games is a conjunction of two binary clauses with all variables up with new classes of strict games that have unique universally quantified. So we implemented a program pure Nash equilibria, where a game is strict if for that examines all these universally quantified conjunctions of both player different profiles have different payoffs.

In this paper, we present a novel approach to the evaluation of propositional answer-set programs. In particular, for programs with bounded treewidth, our algorithm is capable of (i) computing the number of answer sets in linear time and (ii) enumerating all answer sets with linear delay. Our algorithm relies on dynamic programming, which so far has not been applied to ASP-problems. Therefore, our approach significantly differs from standard ASP-systems which implement techniques stemming from SAT or CSP, and thus usually do not exploit fixed parameter properties of the programs. We provide first experimental results which underline that, for programs with low treewidth, already a prototypical implementation is competitive compared to state-of-the-art systems.

First order decision diagrams (FODD) were recently introduced as a compact knowledge representation expressing functions over relational structures. FODDs represent numerical functions that, when constrained to the Boolean range, use only existential quantification. Previous work developed a set of operations over FODDs, showed how they can be used to solve relational Markov decision processes (RMDP) using dynamic programming algorithms, and demonstrated their success in solving stochastic planning problems from the International Planning Competition in the system FODD-Planner. A crucial ingredient of this scheme is a set of operations to remove redundancy in decision diagrams, thus keeping them compact. This paper makes three contributions. First, we introduce Generalized FODDs (GFODD) and combination algorithms for them, generalizing FODDs to arbitrary quantification. Second, we show how GFODDs can be used in principle to solve RMDPs with arbitrary quantification, and develop a particularly promising case where an arbitrary number of existential quantifiers is followed by an arbitrary number of universal quantifiers. Third, we develop a new approach to reduce FODDs and GFODDs using model checking. This yields a reduction that is complete for FODDs and provides a sound reduction procedure for GFODDs.

This paper provides a decentralized data model and associated algorithms for peer data management systems (PDMS) based on the DL-liteR description logic. Our approach relies on reducing query reformulation and consistency checking for DL-liteR into reasoning in propositional logic. This enables a straightforward deployment of DL-liteR PDMSs on top of SomeWhere, a scalable propositional peer-to-peer inference system. We also show how to use the state-of-the-art Minicon algorithm for rewriting queries using views in DL-liteR in the centralized and decentralized cases.

Local pattern mining is concerned with finding the set of patterns that satisfy a constraint in a database. We study local pattern mining in the context of ProbLog, a probabilistic Prolog system, and introduce an approach for finding correlated patterns in the form of queries in such a Prolog system. The approach combines principles of inductive logic programming, data mining and statistical relational learning. Experiments on a challenging biological network mining task provide evidence for the interestingness of the approach.

We present an unified methodology for representation and development of dialectical proof procedures in both abstract and assumption-based argumentation based on the notions of legal environments and dispute derivation. A legal environment specifies the legal moves of the dispute parties while a dispute derivation describes the procedure structure. A key insight of this paper is that the opponent moves determine the soundness of a dispute while its completeness depends on the proponent moves.