A Tableaux Calculus for Reducing Proof Size

A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It is shown that the obtained proof procedure is sound, refutationally complete and allows to reduce the size of the tableau by an exponential factor. The approach is compatible with all usual refinements of tableaux.Comment: Technical Repor

Логіки, орієнтовані на специфікації програм

Розглянуті композиційно-номінативні логіки, орієнтовані на специфікації програм. Такі логіки будуються в семантико- синтаксичному стилі на основі композиційно-номінативного підходу. Пропонується спектр композиційно-номінативних логік різних рівнів абстрактності та загальності. Для логік еквітонних квазіарних предикатів на основі секвенційних числень доведені тео- реми про визначність. На базі аксіоматичної системи специфікацій програм над метаномінативними даними побудовано прототип системи автоматизації доведення теорем теорії МНД.Composition nominative logics oriented on program specification are considered. Such logics based on composition nominative approach are constructed in a semantic-syntactic style. The spectrum of logics of various abstraction and generality levels is developed. The definability theorems are proved based on the sequent calculi for logics of equitone quasiare predicates. The prototype of automatic theorem prover is constructed for the axiomatic system of program specification over metanominative data

The Pocket Reasoner -- Automatic Reasoning on Small Devices

Automated reasoning in classical first-order logic is a core research field in Artificial Intelligence. Most of the fully automated reasoning tools are large and complex systems implementing proof search methods that have significant memory requirements. This paper presents an automated reasoning tool implemented on an iPod Nano. It is based on leanCoP, a very compact Prolog implementation of the connection calculus, which operates on the structure of the given formula without generating new subformula instances. Hence, the memory requirements are significantly lower, allowing leanCoP to run on devices with only little (random-access) memory. The paper presents details of the proof search calculus, its implementation, and a practical evaluation of the presented reasoning tool

Prolog Technology Reinforcement Learning Prover: (System Description)

We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP builds on the leanCoP Prolog implementation and adds learning-guided Monte-Carlo Tree Search as done in the rlCoP system. Other components include a Python interface to plCoP and machine learners, and an external proof checker that verifies the validity of plCoP proofs. The toolkit is evaluated on two benchmarks and we demonstrate its extendability by two additions: (1) guidance is extended to reduction steps and (2) the standard leanCoP calculus is extended with rewrite steps and their learned guidance. We argue that the Prolog setting is suitable for combining statistical and symbolic learning methods. The complete toolkit is publicly released. © 2020, Springer Nature Switzerland AG

Range-Restricted Interpolation through Clausal Tableaux

We show how variations of range-restriction and also the Horn property can be passed from inputs to outputs of Craig interpolation in first-order logic. The proof system is clausal tableaux, which stems from first-order ATP. Our results are induced by a restriction of the clausal tableau structure, which can be achieved in general by a proof transformation, also if the source proof is by resolution/paramodulation. Primarily addressed applications are query synthesis and reformulation with interpolation. Our methodical approach combines operations on proof structures with the immediate perspective of feasible implementation through incorporating highly optimized first-order provers

Set of support, demodulation, paramodulation: a historical perspective

This article is a tribute to the scientific legacy of automated reasoning pioneer and JAR founder Lawrence T. (Larry) Wos. Larry's main technical contributions were the set-of-support strategy for resolution theorem proving, and the demodulation and paramodulation inference rules for building equality into resolution. Starting from the original definitions of these concepts in Larry's papers, this survey traces their evolution, unearthing the often forgotten trails that connect Larry's original definitions to those that became standard in the field