Only-knowing was originally introduced by Levesque to capture the beliefs of an agent in the sense that its knowledge base is all the agent knows. When a knowledge base contains defaults Levesque also showed an exact correspondence between only-knowing and autoepistemic logic. Later these results were extended by Lakemeyer and Levesque to also capture a variant of autoepistemic logic proposed by Konolige and Reiter's default logic. One of the benefits of such an approach is that various nonmonotonic formalisms can be compared within a single monotonic logic leading, among other things, to the first axiom system for default logic. In this paper, we will bring another large class of nonmonotonic systems, which were first studied by McDermott and Doyle, into the only-knowing fold. Among other things, we will provide the first possible-world semantics for such systems, providing a new perspective on the nature of modal approaches to nonmonotonic reasoning.

Belief revision has been extensively studied in the framework of propositional logic, but just recently revision within fragments of propositional logic has gained attention. Hereby it is not only the belief set and the revision formula which are given within a certain language fragment, but also the result of the revision has to be located in the same fragment. So far, research in this direction has been mainly devoted to the Horn fragment of classical logic. In this work, we present a general approach to define new revision operators derived from known operators (as for instance, Satoh's and Dalal's revision operators), such that the result of the revision remains in the fragment under consideration. Our approach is not limited to the Horn case but applicable to any fragment of propositional logic where the models of the formulas are closed under a Boolean function. Thus we are able to uniformly treat cases as dual-Horn, Krom and affine formulas, as well.

Answer set programming is a programming paradigm where a given problem is formalized as a logic program whose answer sets correspond to the solutions to the problem. In this paper, we link answer set programming with another widely applied paradigm, viz.

The stable model semantics treats a logic program as a mechanism for specifying its intensional predicates. In this paper we discuss a modification of that semantics in which functions, rather than predicates, are intensional. The idea of the new definition comes from nonmonotonic causal logic.

In classical logic, nonBoolean fluents, such as the location of an object and the color of a ball, can be naturally described by functions, but this is not the case with the traditional stable model semantics, where the values of functions are pre-defined, and nonmonotonicity of the semantics is related to minimizing the extents of predicates but has nothing to do with functions. We extend the first-order stable model semantics by Ferraris, Lee and Lifschitz to allow intensional functions. The new formalism is closely related to multi-valued nonmonotonic causal logic, logic programs with intensional functions, and other extensions of logic programs with functions, while keeping similar properties as those of the first-order stable model semantics. We show how to eliminate intensional functions in favor of intensional predicates and vice versa, and use these results to encode fragments of the language in the input language of ASP solvers and CSP solvers.

Reiter's original proposal for default logic is unsatisfactory for open default theories because of Skolemization and grounding. In this paper, we reconsider this long-standing problem and propose a new world view semantics for first-order default logic. Roughly speaking, a world view of a first-order default theory is a maximal collection of structures satisfying the default theory where the default part is fixed by the world view itself. We show how this semantics generalizes classical first-order logic and first-order answer set programming, and we discuss its connections to Reiter's semantics and other related semantics. We also argue that first-order default logic under the world view semantics provides a rich framework for integrating classical logic based and rule based formalisms in the first-order case.

Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such properties is non-obvious and can be challenging indeed. In this paper, we take acyclicity properties into consideration and investigate logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic, and linear programming.

Forgetting has been addressed in various areas in KR, including classical logic, logic programming, modal logic, and description logics. Here, we view forgetting as an abstract operator, independent of the underlying logic. We argue that forgetting amounts to a reduction in the signature of a language of a logic, and that the result of forgetting elements of a signature in a theory is the set of logical consequences over the reduced language. This definition offers several advantages. It provides a uniform approach to forgetting, applicable to any logic with a well-defined consequence relation. Obtained results are thus applicable to all subsumed formal systems, and typically are obtained much more straightforwardly. The approach also leads to insights with respect to specific logics: forgetting in first-order logic is somewhat different from the accepted approach; and the definition applied to logic programs yields a new syntax-independent notion of forgetting.

We present a cognitive design assistance system equipped with analytical capabilities aimed at anticipating architectural building design performance with respect to people-centred functional design goals. The paper focuses on the system capability to generate "narratives of visuo-locomotive user experience" from digital computer-aided architecture design (CAAD) models. The system is based on an underlying declarative narrative representation and computation framework pertaining to conceptual, geometric, and qualitative spatial knowledge. The semantics of the declarative narrative model, i.e., the overall representation and computation model, is founded on: (a).

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.