Importing SMT and Connection proofs as expansion trees

Different automated theorem provers reason in various deductive systems and, thus, produce proof objects which are in general not compatible. To understand and analyze these objects, one needs to study the corresponding proof theory, and then study the language used to represent proofs, on a prover by prover basis. In this work we present an implementation that takes SMT and Connection proof objects from two different provers and imports them both as expansion trees. By representing the proofs in the same framework, all the algorithms and tools available for expansion trees (compression, visualization, sequent calculus proof construction, proof checking, etc.) can be employed uniformly. The expansion proofs can also be used as a validation tool for the proof objects produced.Comment: In Proceedings PxTP 2015, arXiv:1507.0837

Labelled Superposition for {PLTL}

This paper introduces a new decision procedure for PLTL based on labelled superposition. Its main idea is to treat temporal formulas as infinite sets of purely propositional clauses over an extended signature. These infinite sets are then represented by finite sets of labelled propositional clauses. The new representation enables the replacement of the complex temporal resolution rule, suggested by existing resolution calculi for PLTL, by a fine grained repetition check of finitely saturated labelled clause sets followed by a simple inference. The completeness argument is based on the standard model building idea from superposition. It inherently justifies ordering restrictions, redundancy elimination and effective partial model building. The latter can be directly used to effectively generate counterexamples of non-valid PLTL conjectures out of saturated labelled clause sets in a straightforward way

Subsumed Label Elimination for Maximum Satisfiability

Proceeding volume: 285Peer reviewe

The Apriori Stochastic Dependency Detection (ASDD) algorithm for learning Stochastic logic rules

Apriori Stochastic Dependency Detection (ASDD) is an algorithm for fast induction of stochastic logic rules from a database of observations made by an agent situated in an environment. ASDD is based on features of the Apriori algorithm for mining association rules in large databases of sales transactions [1] and the MSDD algorithm for discovering stochastic dependencies in multiple streams of data [15]. Once these rules have been acquired the Precedence algorithm assigns operator precedence when two or more rules matching the input data are applicable to the same output variable. These algorithms currently learn propositional rules, with future extensions aimed towards learning first-order models. We show that stochastic rules produced by this algorithm are capable of reproducing an accurate world model in a simple predator-prey environment