Canonical (logic) programs (CP) refer to the class of normal programs (LP) augmented with connective not not , and  are equally expressive as propositional formulas (PF). In this paper we address the question of whether CP and PF are succinctly incomparable. Our main result shows that the PARITY problem only has exponential CP representations, while it can be polynomially represented in PF.  In other words, PARITY separates PF from CP. Simply speaking, this means that exponential size blowup is generally inevitable  when  translating a set of PF formulas into a (logically) equivalent CP program (without introducing new variables). Furthermore,  since it has been shown by Lifschitz and  Razborov  that there is also a problem which separates CP from PF (assuming P ⊈ NC 1 poly), it follows that the two formalisms are indeed succinctly incomparable.

Causal models defined in terms of structural equations have proved to be quite a powerful way of representing knowledge regarding causality. However, a number of authors have given examples that seem to show that the Halpern-Pearl (HP) definition of causality (Halpern & Pearl 2005) gives intuitively unreasonable answers. Here it is shown that, for each of these examples, we can give two stories consistent with the description in the example, such that intuitions regarding causality are quite different for each story. By adding additional variables, we can disambiguate the stories. Moreover, in the resulting causal models, the HP definition of causality gives the intuitively correct answer. It is also shown that, by adding extra variables, a modification to the original HP definition made to deal with an example of Hopkins and Pearl (2003) may not be necessary. Given how much can be done by adding extra variables, there might be a concern that the notion of causality is somewhat unstable. Can adding extra variables in a "conservative" way (i.e., maintaining all the relations between the variables in the original model) cause the answer to the question "Is X = x a cause of Y =  y ?" to alternate between "yes" and "no"? Here it is shown that adding an extra variable can change the answer from "yes' to "no", but after that, it cannot cannot change back to "yes".

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.

Planning as Satisfiability is an important approach to Propositional Planning. A serious drawback of the method is its limited scalability, as the instances that arise from large planning problems are often too hard for modern SAT solvers. This work tackles this problem by combining two powerful techniques that aim at decomposing a planning problem into smaller subproblems, so that the satisfiability instances that need to be solved do not grow prohibitively large. The first technique, incremental goal achievement, turns planning into a series of boolean optimization problems, each seeking to maximize the number of goals that are achieved within a limited planning horizon. This is coupled with a second technique, called heuristic guidance, that directs search towards a state which satisfies all goals.

The paper addresses how the information state of an agent relates to the arguments that the agent endorses. Information states are modeled in doxastic logic and arguments by recasting abstract argumentation theory in a modal logic format. The two perspectives are combined by an application of the theory of product logics, delivering sound and complete systems in which the interaction of arguments and beliefs is investigated.

We report on an ongoing research program to develop a formal framework for automated narrative text comprehension, bringing together know-how from research in Artificial Intelligence and the Psychology of Reading and Comprehension. It uses argumentation to capture appropriate solutions to the frame, ramification, and qualification problems, and their generalizations as required for text comprehension. In this first part of the study we concentrate on the central problem of integration of the explicit information from the text narrative with the reader's implicit commonsense world knowledge, and the associated tasks of elaboration and revision.

We introduce dynamic causal calculus, a nonmonotonic formalism that can be viewed as a direct logical counterpart of the action description language C+. We formulate a nonmonotonic semantics of the associated causal language, and compare this semantics with the indirect, two-stage semantics for C+, given in (Giunchiglia et al 2004). It will be shown, in particular, that the suggested semantics allows us to alleviate syntactic distinctions between propositional atoms, maintained by C+, as well as type restrictions imposed on its causal laws. We will describe also a logical formalism of dynamic causal inference that constitutes a complete description of the logic that is adequate for this dynamic calculus.

Graphical belief models are compact and powerful tools for representing and reasoning under uncertainty. Possibilistic networks are graphical belief models based on possibility theory. In this paper, we address reasoning under uncertain inputs in both quantitative and qualitative possibilistic networks. More precisely, we first provide possibilistic counterparts of Pearl's methods of virtual evidence then compare them with the possibilistic counterparts of Jeffrey's rule of conditioning. As in the probabilistic setting, the two methods are shown to be equivalent in the quantitative setting regarding the existence and uniqueness of the solution. However in the qualitative setting, Pearl's method of virtual evidence which applies directly on graphical models disagrees with Jeffrey's rule and the virtual evidence method. The paper provides the precise situations where the methods are not equivalent. Finally, the paper addresses related issues like transformations from one method to another and commutativity.

In Description Logic (DL) knowledge bases (KBs) information is typically captured by crisp concepts. For many applications, querying the KB by crisp query concepts is too restrictive. A controlled way of gradually relaxing a query concept can be achieved by the use of concept similarity measures. In this paper we formalize the task of instance query answering for crisp DL KBs using concepts relaxed by concept similarity measures. We investigate computation algorithms for this task in the DL EL, their complexity and properties for the employed similarity measure regarding whether unfoldable or general TBoxes are used.

A strong intuition for AGM belief change operations, Gärdenfors suggests, is that formulas that are independent of a change should remain intact. Based on this intuition, Fariñas and Herzig axiomatize a dependence relation w.r.t. a belief set, and formalize the connection between dependence and belief change. In this paper, we introduce base dependence as a relation between formulas w.r.t. a belief base. After an axiomatization of base dependence, we formalize the connection between base dependence and a particular belief base change operation, saturated kernel contraction. Moreover, we prove that base dependence is a reversible generalization of Fariñas and Herzig’s dependence. That is, in the special case when the underlying belief base is deductively closed (i.e., it is a belief set), base dependence reduces to dependence. Finally, an intriguing feature of Fariñas and Herzig’s formalism is that it meets other criteria for dependence, namely, Keynes’ conjunction criterion for dependence (CCD) and Gärdenfors’ conjunction criterion for independence (CCI). We show that our base dependence formalism also meets these criteria. More interestingly, we offer a more specific criterion that implies both CCD and CCI, and show our base dependence formalism also meets this new criterion.