It is well known that the standard model of knowledge based on possible worlds is subject to the problem of logical omniscience, that is, the agents know all the logical consequences of the ir knowledge [Fagin, Halpern, Moses, and V ardi 1995, Chapter 9]. Thu s, possible-world definitions of knowledge make it difficult to reason about the knowledge tha t agents need to explicitly compute in order to make decisions and perform actions, or to capture si tuations where agents want to reason about the knowledge that other agents need to explicitly com pute in order to perform actions. This observation leads to a distinction between two forms of knowledge, implicit knowledge and explicit knowledge (or resource-bounded knowledge), a distinction long recog nized [Rosenschein 1985]. The classical AI approach known as the interpreted symbolic structures approach, where knowledge is based on information stored in data structures of the agent, can be seen as an instance of explicit knowledge. In contrast, the situated automata approach, which interprets knowledge based on information carried by the state of the machine, can be seen as an instance of implicit knowledge. Levesque [1984] makes a similar distinction bet ween implicit belief and explicit belief. While the possible-worlds approach is taken as the standard model for implicit knowledge, there is no standard model for explicit knowledge.

It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be constructed by incrementally constructing models for each level. Similar results exist for other non-monotonic formalisms, such as auto-epistemic logic and default logic. In this work, we present a general, algebraicsplitting theory for logics with a fixpoint semantics. Together with the framework of approximation theory, a general fixpoint theory for arbitrary operators, this gives us a uniform and powerful way of deriving splitting results for each logic with a fixpoint semantics. We demonstrate the usefulness of these results, by generalizing existing results for logic programming, auto-epistemic logic and default logic.

Sequential decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameter-free theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline how the AIXI model can formally solve a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXItl that is still effectively more intelligent than any other time t and length l bounded agent. The computation time of AIXItl is of the order t x 2^l. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches.

Because query execution is the most crucial part of Inductive Logic Programming (ILP) algorithms, a lot of effort is invested in developing faster execution mechanisms. These execution mechanisms typically have a low-level implementation, making them hard to debug. Moreover, other factors such as the complexity of the problems handled by ILP algorithms and size of the code base of ILP data mining systems make debugging at this level a very difficult job. In this work, we present the trace-based debugging approach currently used in the development of new execution mechanisms in hipP, the engine underlying the ACE Data Mining system. This debugger uses the delta debugging algorithm to automatically reduce the total time needed to expose bugs in ILP execution, thus making manual debugging step much lighter.

This paper presents a property of propositional theories un der the answer sets semantics (called Equilibrium Logic for this general syntax): any theory can always be reexpress ed as a strongly equivalent disjunctive logic program, possib ly with negation in the head. We provide two different proofs for this result: one involvin g a syntactic transformation, and one that constructs a program starting from the counterm odels of the theory in the intermediate logic of here-and-there.

Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program's constants. We define a fixed point logic (FPL) extension of Clark's completion such that open answer sets correspond to models of FPL formulas and identify a syntactic subclass of programs, called (loosely) guarded programs. Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (mu(L)GF). Moreover, we reduce normal closed ASP to loosely guarded OASP, enabling for the first time, a characterization of an answer set semantics by muLGF formulas. We further extend the open answer set semantics for programs with generalized literals. Such generalized programs (gPs) have interesting properties, e.g., the ability to express infinity axioms. We restrict the syntax of gPs such that both rules and generalized literals are guarded. Via a translation to guarded fixed point logic, we deduce 2-exptime-completeness of satisfiability checking in such guarded gPs (GgPs). Bound GgPs are restricted GgPs with exptime-complete satisfiability checking, but still sufficiently expressive to optimally simulate computation tree logic (CTL). We translate Datalog lite programs to GgPs, establishing equivalence of GgPs under an open answer set semantics, alternation-free muGF, and Datalog lite.

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, "truth" means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and completeness with respect to the semantics of CL. Conservatively extending classical predicate calculus and offering considerable additional expressive and deductive power, CL12 presents a reasonable, computationally meaningful, constructive alternative to classical logic as a basis for applied theories. To obtain a model example of such theories, this paper rebuilds the traditional, classical-logic-based Peano arithmetic into a computability-logic-based counterpart. Among the purposes of the present contribution is to provide a starting point for what, as the author wishes to hope, might become a new line of research with a potential of interesting findings -- an exploration of the presumably quite unusual metatheory of CL-based arithmetic and other CL-based applied systems.

Verification that agent communication protocols have desirable properties or do not have undesirable properties is an important issue in agent systems where agents intend to communicate using such protocols. In this paper we explore the use of model checkers to verify properties of agent communication protocols, with these properties expressed as formulae in temporal logic.  We illustrate our approach using a recently-proposed protocol for agent dialogues over commands, a protocol that permits the agents to present questions, challenges and arguments for or against compliance with a command.

Argumentation Frameworks (AFs) provide a fruitful basis for exploring issues of defeasible reasoning. Their power largely derives from the abstract nature of the arguments within the framework, where arguments are atomic nodes in an undifferentiated relation of attack. This abstraction conceals different conceptions of argument, and concrete instantiations encounter difficulties as a result of conflating these conceptions. We distinguish three distinct senses of the term. We provide an approach to instantiating AFs in which the nodes are restricted to literals and rules, encoding the underlying theory directly. Arguments, in each of the three senses, then emerge from this framework as distinctive structures of nodes and paths. Our framework retains the theoretical and computational benefits of an abstract AF, while keeping notions distinct which are conflated in other approaches to instantiation.

Defeasible Logic Programming (DELP) is a formalism that extends declarative programming to capture defeasible reasoning. Its inference mechanism, upon a query on a literal in a program, answers by indicating whether or not it is warranted in an argumentation process. While the properties of DELP are well known, some of its basic elements can be redefined in order to shed light on some of the subtleties of the warrant process. We will discuss these alternative definitions and the cases in which they provide a better performance.