The duality between conflicts and diagnoses in the field of diagnosis, or between plans and landmarks in the field of planning, or between unsatisfiable cores and minimal co-satisfiable sets in SAT or CSP solving, has been known for many years. Recent work in these communities (Davies and Bacchus, CP 2011, Bonet and Helmert, ECAI 2010, Haslum et al., ICAPS 2012, Stern et al., AAAI 2012) has brought it to the fore as a topic of current interest. The present paper lays out the set-theoretic basis of the concept, and introduces a generic implementation of an algorithm based on it. This algorithm provides a method for converting decision procedures into optimisation ones across a wide range of applications without the need to rewrite the decision procedure implementations. Initial experimental validation shows good performance on a number of benchmark problems from AI planning.

CNF simplifiers play a very important role in minimising structured problem hardness. Although they can be used in an in-search process, most of them serve in a pre-search phase and rely on one form or another of resolution. Based on our understanding about problem structure, in the paper, we extend the single pre-search process to a multiple one in order to further simplify the hard structure in a problem. This extension boosts the performance of state-of-the-art clause learning and lookahead based SAT solvers when solving both satisfiable and unsatisfiable instances of many real-world hard combinatorial problems.

A decision process in which rewards depend on history rather than merely on the current state is called a decision process with non-Markovian rewards (NMRDP). In decision-theoretic planning, where many desirable behaviours are more naturally expressed as properties of execution sequences rather than as properties of states, NMRDPs form a more natural model than the commonly adopted fully Markovian decision process (MDP) model. While the more tractable solution methods developed for MDPs do not directly apply in the presence of non-Markovian rewards, a number of solution methods for NMRDPs have been proposed in the literature. These all exploit a compact specification of the non-Markovian reward function in temporal logic, to automatically translate the NMRDP into an equivalent MDP which is solved using efficient MDP solution methods. This paper presents NMRDPP (Non-Markovian Reward Decision Process Planner), a software platform for the development and experimentation of methods for decision-theoretic planning with non-Markovian rewards. The current version of NMRDPP implements, under a single interface, a family of methods based on existing as well as new approaches which we describe in detail. These include dynamic programming, heuristic search, and structured methods. Using NMRDPP, we compare the methods and identify certain problem features that affect their performance. NMRDPP's treatment of non-Markovian rewards is inspired by the treatment of domain-specific search control knowledge in the TLPlan planner, which it incorporates as a special case. In the First International Probabilistic Planning Competition, NMRDPP was able to compete and perform well in both the domain-independent and hand-coded tracks, using search control knowledge in the latter.

Abstract It is shown that there are exactly six normal DeMorgan monoids generated by the idntity element alone. The free DeMorgan monoid with no generators but the identity is characterised and shown to have exactly three thousand and eighty-eight elements. This result solves the “Ackermann constant problem” of describing the structure of sentential constants in the logic R.