In a seminal paper, Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. Earlier works by Moore, Scherl and Levesque extended the situation calculus to account for knowledge. In this paper, we study progression of knowledge in the situation calculus. We first adapt the concept of bisimulation from modal logic and extend Lin and Reiter's notion of progression to accommodate knowledge. We show that for physical actions, progression of knowledge reduces to forgetting predicates in first-order modal logic. We identify a class of first-order modal formulas for which forgetting an atom is definable in first-order modal logic. This class of formulas goes beyond formulas without quantifying-in. We also identify a simple case where forgetting a predicate reduces to forgetting a finite number of atoms. Thus we are able to show that for local-effect physical actions, when the initial KB is a formula in this class, progression of knowledge is definable in first-order modal logic. Finally, we extend our results to the multi-agent case.

Learning concepts via instruction and expository texts is an important problem for modeling human learning and for making autonomous AI systems. This paper describes a computational model of the self-explanation effect, whereby conceptual knowledge is repaired by integrating and explaining new material. Our model represents conceptual knowledge with compositional model fragments, which are used to explain new material via model formulation. Preferences are computed over explanations and conceptual knowledge, along several dimensions. These preferences guide knowledge integration and question-answering. Our simulation learns about the human circulatory system, using facts from a circulatory system passage used in a previous cognitive psychology experiment. We analyze the simulation’s performance, showing that individual differences in sequences of models learned by students can be explained by different parameter settings in our model.

We present a unifying approach to the efficient evaluation of propositional answer-set programs. Our approach is based on backdoors which are small sets of atoms that represent "clever reasoning shortcuts" through the search space. The concept of backdoors is widely used in the areas of propositional satisfiability and constraint satisfaction. We show how this concept can be adapted to the nonmonotonic setting and how it allows to augment various known tractable subproblems, such as the evaluation of Horn and acyclic programs. In order to use backdoors we need to find them first. We utilize recent advances in fixed-parameter algorithmics to detect small backdoors. This implies fixed-parameter tractability of the evaluation of propositional answer-set programs, parameterized by the size of backdoors. Hence backdoor size provides a structural parameter similar to the treewidth parameter previously considered. We show that backdoor size and treewidth are incomparable, hence there are instances that are hard for one and easy for the other parameter. We complement our theoretical results with first empirical results.

This paper investigates belief revision where the underlying logic is that governing Horn clauses. It proves to be the case that classical (AGM) belief revision doesn’t immediately generalise to the Horn case. In particular, a standard construction based on a total preorder over possible worlds may violate the accepted (AGM) postulates. Conversely, Horn revision functions in the obvious extension to the AGM approach are not captured by total preorders over possible worlds. We address these difficulties by first restricting the semantic construction to "well behaved" orderings; and second, by augmenting the revision postulates by an additional postulate. This additional postulate is redundant in the AGM approach but not in the Horn case. In a representation result we show that these two approaches coincide. Arguably this work is interesting for several reasons. It extends AGM revision to inferentially-weaker Horn theories; hence it sheds light on the theoretical underpinnings of belief change, as well as generalising the AGM paradigm. Thus, this work is relevant to revision in areas that employ Horn clauses, such as deductive databases and logic programming, as well as areas in which inference is weaker than classical logic, such as in description logic.

We identify a new representation of propositional knowledge bases, the Sentential Decision Diagram SDD, which is interesting for a number of reasons. First, it is canonical in the presence of additional properties that resemble reduction rules of OBDDs. Second, SDDs can be combined using any Boolean operator in polytime. Third, CNFs with n variables and treewidth w have canonical SDDs of size O ( n 2 w ), which is tighter than the bound on OBDDs based on pathwidth. Finally, every OBDD is an SDD. Hence, working with the latter does not preclude the former.

One of main difficulties of multi-dimensional packing problems is the fragmentation of free space into several unusable small parts after a few items are packed. This study proposes a defragmentation technique to combine the fragmented space into a continuous usable space, which potentially allows the packing of additional items. We illustrate the effectiveness of this technique on the two- and three-dimensional Bin Packing Problems. In conjunction with a bin shuffling strategy for incremental improvement, our resultant algorithm outperforms all leading meta-heuristic approaches.

Heuristics are crucial tools in decreasing search effort in varied fields of AI. In order to be effective, a heuristic must be efficient to compute, as well as provide useful information to the search algorithm. However, some well-known heuristics which do well in reducing backtracking are so heavy that the gain of deploying them in a search algorithm might be outweighed by their overhead. We propose a rational metareasoning approach to decide when to deploy heuristics, using CSP backtracking search as a case study. In particular, a value of information approach is taken to adaptive deployment of solution-count estimation heuristics for value ordering. Empirical results show that indeed the proposed mechanism successfully balances the tradeoff between decreasing backtracking and heuristic computational overhead, resulting in a significant overall search time reduction.

We develop a real-time algorithm based on a Monte-Carlo game tree search for solving a quantified constraint satisfaction problem (QCSP), which is a CSP where some variables are universally quantified. A universally quantified variable represents a choice of nature or an adversary. The goal of a QCSP is to make a robust plan against an adversary. However, obtaining a complete plan off-line is intractable when the size of the problem becomes large. Thus, we need to develop a real-time algorithm that sequentially selects a promising value at each deadline. Such a problem has been considered in the field of game tree search. In a standard game tree search algorithm, developing a good static evaluation function is crucial. However, developing a good static evaluation function for a QCSP is very difficult since it must estimate the possibility that a partially assigned QCSP is solvable. Thus, we apply a Monte-Carlo game tree search technique called UCT. However, the simple application of the UCT algorithm does not work since the player and the adversary are asymmetric, i.e., finding a game sequence where the player wins is very rare. We overcome this difficulty by introducing constraint propagation techniques. We experimentally compare the winning probability of our UCT-based algorithm and the state-of-the-art alpha-beta search algorithm. Our results show that our algorithm outperforms the state-of-the-art algorithm in large-scale problems.

This paper proposes the integration of the resolution rule for Max-SAT with unsatisfiability-based Max-SAT solvers. First, we show that the resolution rule for Max-SAT can be safely applied as dictated by the resolution proof associated with an unsatisfiable core when such proof is read-once, that is, each clause is used at most once in the resolution process. Second, we study how this property can be integrated in an unsatisfiability-based solver. In particular, the resolution rule for Max-SAT is applied to read-once proofs or to read-once subparts of a general proof. Finally, we perform an empirical investigation on structured instances from recent Max-SAT evaluations. Preliminary results show that the use of read-once resolution substantially improves the performance of the solver.

We address a dynamic decision problem in which decision makers must pay some costs when they change their decisions along the way. We formalize this problem as Dynamic SAT (DynSAT) with decision change costs, whose goal is to find a sequence of models that minimize the aggregation of the costs for changing variables. We provide two solutions to solve a specific case of this problem. The first uses a Weighted Partial MaxSAT solver after we encode the entire problem as a WeightedPartial MaxSAT problem. The second solution, which we believe is novel, uses the Lagrangian decomposition technique that divides the entire problem into sub-problems, each of which can be separately solved by an exact Weighted Partial MaxSATsolver, and produces both lower and upper bounds on the optimal in an anytime manner. To compare the performance of these solvers, we experimentedon the random problem and the target trackingproblem. The experimental results show that a solver based on Lagrangian decomposition performs better for the random problem and competitively for the target tracking problem.