ATP and Presentation Service for Mizar Formalizations

This paper describes the Automated Reasoning for Mizar (MizAR) service, which integrates several automated reasoning, artificial intelligence, and presentation tools with Mizar and its authoring environment. The service provides ATP assistance to Mizar authors in finding and explaining proofs, and offers generation of Mizar problems as challenges to ATP systems. The service is based on a sound translation from the Mizar language to that of first-order ATP systems, and relies on the recent progress in application of ATP systems in large theories containing tens of thousands of available facts. We present the main features of MizAR services, followed by an account of initial experiments in finding proofs with the ATP assistance. Our initial experience indicates that the tool offers substantial help in exploring the Mizar library and in preparing new Mizar articles

Evaluating general purpose automated theorem proving systems

AbstractA key concern of ATP research is the development of more powerful systems, capable of solving more difficult problems within the same resource limits. In order to build more powerful systems, it is important to understand which systems, and hence which techniques, work well for what types of problems. This paper deals with the empirical evaluation of general purpose ATP systems, to determine which systems work well for what types of problems. This requires also dealing with the issues of assigning ATP problems into classes that are reasonably homogeneous with respect to the ATP systems that (attempt to) solve the problems, and assigning ratings to problems based on their difficulty

Larry Wos - Visions of automated reasoning

This paper celebrates the scientific discoveries and the service to the automated reasoning community of Lawrence (Larry) T. Wos, who passed away in August 2020. The narrative covers Larry's most long-lasting ideas about inference rules and search strategies for theorem proving, his work on applications of theorem proving, and a collection of personal memories and anecdotes that let readers appreciate Larry's personality and enthusiasm for automated reasoning

Improving probability selection based weights for satisfiability problems

Boolean Satisfiability problem (SAT) plays a prominent role in many domains of computer science and artificial intelligence due to its significant importance in both theory and applications. Algorithms for solving SAT problems can be categorized into two main classes: complete algorithms and incomplete algorithms (typically stochastic local search (SLS) algorithms). SLS algorithms are among the most effective for solving uniform random SAT problems, while hybrid algorithms achieved great breakthroughs for solving hard random SAT (HRS) problem recently. However, there is a lack of algorithms that can effectively solve both uniform random SAT and HRS problems. In this paper, a new SLS algorithm named SelectNTS is proposed aiming at solving both uniform random SAT and HRS problem effectively. SelectNTS is essentially an improved probability selection based local search algorithm, the core of which includes new clause and variable selection heuristics: a new clause weighting scheme and a biased random walk strategy are utilized to select a clause, while a new probability selection strategy with the variation of configuration checking strategy is used to select a variable. Extensive experimental results show that SelectNTS outperforms the state-of-the-art random SAT algorithms and hybrid algorithms in solving both uniform random SAT and HRS problems effectively

TH1: The TPTP Typed Higher-Order Form with Rank-1 Polymorphism

Abstract The TPTP world is a well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems for classical logics. The TPTP language is one of the keys to the success of the TPTP world. Originally the TPTP world supported only first-order clause normal form (CNF). Over the years support for full first-order form (FOF), monomorphic typed firstorder form (TF0), rank-1 polymorphic typed first-order form (TF1), and monomorphic typed higher-order form (TH0) have been added. The TF0, TF1, and TH0 languages also include constructs for arithmetic. This paper introduces the TH1 form, an extension of TH0 with TF1-style rank-1 polymorphism. TH1 is designed to be easy to process by existing reasoning tools that support ML-style polymorphism. The hope is that TH1 will be implemented in many popular ATP systems for typed higher-order logic

Representation, Verification, and Visualization of Tarskian Interpretations for Typed First-order Logic

peer reviewedThis paper describes a new format for representing Tarskian-style interpretations for formulae in typed first-order logic, using the TPTP TF0 language. It further describes a technique and an implemented tool for verifying models using this representation, and a tool for visualizing interpretations. The research contributes to the advancement of automated reasoning technology for model finding, which has several applications, including verification

How much do delayed health care seeking, delayed care provision and diversion from primary care contribute to the transmission of STIs

Objectives: To explore the changing pattern of condom use from 1990 to 2000; to identify sociodemographic and behavioural factors associated with condom use; and reasons for condom use in 2000. Methods: Large probability sample surveys administered among those resident in Britain aged 16–44 (n = 13 765 in 1990, n = 11 161 in 2000). Face to face interviews with self completion components collected sociodemographic, behavioural, and attitudinal data. Results: Condom use in the past year among sexually active 16–24 year old men increased from 61.0% in 1990 to 82.1% in 2000 (p<0.0001), and from 42.0% to 63.2% (p<0.0001) among women of the same age, with smaller increases among older age groups. Among individuals reporting at least two partners in the previous 4 week period, approximately two thirds reported inconsistent or no condom use (63.1% (95% CI 55.9% to 69.8%) of the men and 68.5% (95% CI 57.6% to 77.7%) of the women). Conclusions: Rates of condom use increased substantially between 1990 and 2000, particularly among young people. However, inconsistent condom use by individuals with high rates of partner acquisition may contribute significantly to the recent resurgence in STIs. This group is an important target for intensive and specific sexual health interventions