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.

First-order model counting emerged recently as a novel reasoning task, at the core of efficient algorithms for probabilistic logics. We present a Skolemization algorithm for model counting problems that eliminates existential quantifiers from a first-order logic theory without changing its weighted model count. For certain subsets of first-order logic, lifted model counters were shown to run in time polynomial in the number of objects in the domain of discourse, where propositional model counters require exponential time. However, these guarantees apply only to Skolem normal form theories (i.e., no existential quantifiers) as the presence of existential quantifiers reduces lifted model counters to propositional ones. Since textbook Skolemization is not sound for model counting, these restrictions precluded efficient model counting for directed models, such as probabilistic logic programs, which rely on existential quantification. Our Skolemization procedure extends the applicability of first-order model counters to these representations. Moreover, it simplifies the design of lifted model counting algorithms.

In the past, there have been several attempts to explain logic programming under the well-founded semantics as a logic of inductive definitions. A weakness in all is the absence of an obvious connection between how we understand various types of informal inductive definitions in mathematical text and the complex mathematics of the well-founded semantics. We formalize the induction process in the most common principles and prove that the well-founded model construction generalizes them all.

Extensional higher-order logic programming has been recently proposed as an interesting extension of classical logic programming. An important characteristic of the new paradigm is that it preserves all the well-known properties oftraditional logic programming. In this paper we enhance extensional higher-order logic programming with constructive negation. We argue that the main ideas underlying constructive negation are quite close to the existing proof procedurefor extensional higher-order logic programming and for this reason the two notions amalgamate quite conveniently. We demonstrate the soundness of the resulting proof procedure and describe an actual implementation of a language that embodies the above ideas. In this way we obtain the first (to our knowledge) higher-order logic programming language supporting constructive negation and offering a new style of programming that genuinely extends that of traditional logic programming.

Most logic-based machine learning algorithms rely on an Occamist bias where textual complexity of hypotheses is minimised. Within Inductive Logic Programming (ILP), this approach fails to distinguish between the efficiencies of hypothesised programs, such as quick sort (O(n log n)) and bubble sort (O(n2)).

We consider a simple language for writing causal action theories, and postulate several properties for the state transition models of these theories. We then consider some possible embeddings of these causal action theories in some other action formalisms, and their implementations in logic programs with answer set semantics. In particular, we propose to consider what we call permissible translations from these causal action theories to logic programs. We identify two sets of properties, and prove that for each set, there is only one permissible translation, under strong equivalence, that can satisfy all properties in the set. As it turns out, for one set, the unique permissible translation is essentially the same as Balduccini and Gelfond's translation from Gelfond and Lifschitz's action language B to logic programs. For the other, it is essentially the same as Lifschitz and Turner's translation from the action language C to logic programs. This work provides a new perspective on understanding, evaluating and comparing action languages by using sets of properties instead of examples. It will be interesting to see if other action languages can be similarly characterized, and whether new action formalisms can be defined using different sets of properties.

Preference Inference involves inferring additional user preferences from elicited or observed preferences, based on assumptions regarding the form of the user's preference relation. In this paper we consider a situation in which alternatives have an associated vector of costs, each component corresponding to a different criterion, and are compared using a kind of lexicographic order, similar to the way alternatives are compared in a Hierarchical Constraint Logic Programming model. It is assumed that the user has some (unknown) importance ordering on criteria, and that to compare two alternatives, firstly, the combined cost of each alternative with respect to the most important criteria are compared; only if these combined costs are equal, are the next most important criteria considered. The preference inference problem then consists of determining whether a preference statement can be inferred from a set of input preferences. We show that this problem is co-NP-complete, even if one restricts the cardinality of the equal-importance sets to have at most two elements, and one only considers non-strict preferences. However, it is polynomial if it is assumed that the user's ordering of criteria is a total ordering; it is also polynomial if the sets of equally important criteria are all equivalence classes of a given fixed equivalence relation. We give an efficient polynomial algorithm for these cases, which also throws light on the structure of the inference.

Fundamental to reasoning about actions and beliefs is the projection problem: to decide what is believed after a sequence of actions is performed. Progression is one widely applied technique to solve this problem. In this paper we propose a novel framework for computing progression in the epistemic situation calculus. In particular, we model an agent's preferential belief structure using conditional statements and provide a technique for updating these conditional statements as actions are performed and sensing information is received. Moreover, we show, by using the concepts of natural revision and only-believing, that the progression of a conditional knowledge base can be represented by only-believing the revised set of conditional statements. These results lay the foundations for feasible belief progression due to the unique-model property of only-believing.