Jan Jakubův

BliStrTune: hierarchical invention of theorem proving strategies

Inventing targeted proof search strategies for specific problem sets is a difficult task. State-of-the-art automated theorem provers (ATPs) such as E allow a large number of user-specified proof search strategies described in a rich domain specific language. Several machine learning methods that invent strategies automatically for ATPs were proposed previously. One of them is the Blind Strategymaker (BliStr), a system for automated invention of ATP strategies. In this paper we introduce BliStrTune -- a hierarchical extension of BliStr. BliStrTune allows exploring much larger space of E strategies by interleaving search for high-level parameters with their fine-tuning. We use BliStrTune to invent new strategies based also on new clause weight functions targeted at problems from large ITP libraries. We show that the new strategies significantly improve Es performance in solving problems from the Mizar Mathematical Library.

Extending E Prover with Similarity Based Clause Selection Strategies

E prover is a state-of-the-art theorem prover for first-order logic with equality. E prover is built around a saturation loop, where new clauses are derived by inference rules from previously derived clauses. Selection of clauses for the inference provides the main source of non-determinism and an important choice-point of the loop where the right choice can dramatically influence the proof search. In this work we extend E Prover with several new clause selection strategies based on similarity of a clause with the conjecture. In particular, clauses which are more related to the conjecture are preferred. We implement different strategies that define the relationship with a conjecture in different ways. We provide an implementation of the proposed selection strategies and we evaluate their efficiency on an extensive benchmark set.

ENIGMA: Efficient Learning-Based Inference Guiding Machine

ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers. Clauses from many previous proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, classifying a clause as useful or un-useful for the proof search. This learned classification is used to guide next proof searches prioritizing useful clauses among other generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E’s performance.

Recursive Reductions of Action Dependencies for Coordination-Based Multiagent Planning

Currently the most efficient distributed multiagent planning scheme for deterministic models is based on coordination of local agents’ plans. In such a scheme, behavior of other agents is modeled using projections of their actions stripped of all private information. The planning scheme does not require any additional information, however using such can be beneficial for planning efficiency. Dependencies among the projected public actions caused by sequences of local private actions represent one particular type of such information.

Towards a Unified Ordering for Superposition-Based Automated Reasoning.

We propose an extension of the automated theorem prover E by the weighted path ordering. Weighted path ordering is theoretically stronger than all the orderings used in E-prover, however its parametrization is more involved than those normally used in automated reasoning. In particular, it depends on a term algebra. We discuss how the parameters for the ordering can be proposed automatically for particular theorem proving problem strategies. We integrate the ordering in E-prover and perform an evaluation on the standard theorem proving benchmarks. The ordering is complementary to the ones used in E prover so far.

ProofWatch: Watchlist Guidance for Large Theories in E

Watchlist (also hint list) is a mechanism that allows related proofs to guide a proof search for a new conjecture. This mechanism has been used with the Otter and Prover9 theorem provers, both for interactive formalizations and for human-assisted proving of open conjectures in small theories. In this work we explore the use of watchlists in large theories coming from first-order translations of large ITP libraries, aiming at improving hammer-style automation by smarter internal guidance of the ATP systems. In particular, we (i) design watchlist-based clause evaluation heuristics inside the E ATP system, and (ii) develop new proof guiding algorithms that load many previous proofs inside the ATP and focus the proof search using a dynamically updated notion of proof matching. The methods are evaluated on a large set of problems coming from the Mizar library, showing significant improvement of E’s standard portfolio of strategies, and also of the previous best set of strategies invented for Mizar by evolutionary methods.

Enhancing ENIGMA Given Clause Guidance

ENIGMA is an efficient implementation of learning-based guidance for given clause selection in saturation-based automated theorem provers. In this work, we describe several additions to this method. This includes better clause features, adding conjecture features as the proof state characterization, better data pre-processing, and repeated model learning. The enhanced ENIGMA is evaluated on the MPTP2078 dataset, showing significant improvements.

Extensibility Based Multiagent Planner with Plan Diversity Metrics

Coordinated sequential decision making of a team of cooperative agents is described by principles of multiagent planning. In this work, we extend the MA-Strips formalism with the notion of extensibility and reuse a well-known initiator–participants scheme for agent negotiation. A multiagent extension of the Generate-And-Test principle is used to distributively search for a coordinated multiagent plan. The generate part uses a novel plan quality estimation technique based on metrics often used in the field of diverse planning. The test part builds upon planning with landmark actions by compilation to classic planning. We designed a new multiagent planning domain which illustrates the basic properties of the proposed multiagent planning approach. Finally, our approach was experimentally evaluated on four classic IPC benchmark domains modified for multiagent settings. The results show (1) which combination of plan quality estimation and (2) which diversity metrics provide the best planning efficiency.

Using Process Calculi for Plan Verification in Multiagent Planning

Multiagent planning is a coordination technique used for deliberative acting of a team of agents. One of vital planning techniques uses declarative description of agents’ plans based on Finite State Machines and their later coordination by intersection of such machines with successive verification of the resulting joint plans.

From Public Plans to Global Solutions in Multiagent Planning

Multiagent planning addresses the problem of coordinated sequential decision making of a team of cooperative agents. One possible approach to multiagent planning, which proved to be very efficient in practice, is to find an acceptable public plan. The approach works in two stages. At first, a public plan acceptable to all the involved agents is computed. Then, in the second stage, the public solution is extended to a global solution by filling in internal information by every agent. In the recently proposed distributed multiagent planner, the winner of the Competition of Distributed Multiagent Planners (CoDMAP 2015), this principle was utilized, however with unnecessary use of combination of both public and internal information for extension of the public solution.