SEPIA: Search for Proofs Using Inferred Automata

This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These can then be traversed automatically to identify proofs. The SEPIA system is described and its performance evaluated on three Coq datasets. Our results show that SEPIA provides a useful complement to existing automated tactics in Coq.Comment: To appear at 25th International Conference on Automated Deductio

Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers

We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated Deduction, 2015. Proceedings to be published by Springer-Verla

A Paraconsistent Higher Order Logic

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker, Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte

Mining State-Based Models from Proof Corpora

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will lead to a successful proof requires a significant amount of human intervention. This paper presents an automated technique that takes as input examples of successful proofs and infers an Extended Finite State Machine as output. This can in turn be used to generate proofs of new conjectures. Our preliminary experiments show that the inferred models are generally accurate (contain few false-positive sequences) and that representing existing proofs in such a way can be very useful when guiding new ones.Comment: To Appear at Conferences on Intelligent Computer Mathematics 201

A Foundational View on Integration Problems

The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario is often approached from an engineering perspective, we take a foundational view. Based on the generic declarative language MMT, we develop a theoretical framework for system integration using theories and partial theory morphisms. Because MMT permits representations of the meta-logical foundations themselves, this includes integration across logics. We discuss safe and unsafe integration schemes and devise a general form of safe integration

Intellectual and motor development of young adults with congenital hypothyroidism diagnosed by neonatal screening

Contains fulltext : 35756.pdf (publisher's version ) (Open Access)CONTEXT: Long-term follow-up data on cognitive and motor functioning in adult patients with congenital hypothyroidism, diagnosed by neonatal screening, are scarce. Hence, it is still unclear whether the frequently reported cognitive and motor deficits observed during childhood persist in adulthood. OBJECTIVE: The objective of this study was to examine cognitive and motor functioning in young adults with congenital hypothyroidism, born in the first 2 yr after the introduction of the Dutch neonatal screening program. DESIGN/SETTING/PATIENTS: Seventy patients were tested (mean age, 21.5 yr); 49 of them were previously tested at 9.5 yr. The median age at the start of treatment was 28 d (range, 4-293 d). Congenital hypothyroidism was classified as severe, moderate, or mild, according to pretreatment T(4) concentrations. MAIN OUTCOME MEASUREMENT: The main outcome measurement was the influence of the severity of congenital hypothyroidism and age at which T(4) supplementation was started on cognitive and motor outcome. RESULTS: Patients, particularly those with severe congenital hypothyroidism, had significantly higher (i.e. worse) motor scores (total score, 7.8; ball skills, 2.0; balance, 4.1) compared with controls (total score, 3.2; ball skills, 0.7; balance, 1.1), and lower full-scale (95.8), verbal (96.4), and performance (95.6) intelligence quotient (IQ) scores than the normal population. No significant change in IQ from childhood to adulthood was found, and for the majority of patients, motor score classification remained the same. The severity of congenital hypothyroidism, but not the starting day of treatment, was correlated with IQ and motor scores. CONCLUSIONS: It is concluded that the severity of congenital hypothyroidism, but not the timing of treatment initiation, is an important factor determining long-term cognitive and motor outcome. Clearly, detrimental effects on developmental outcome in patients with congenital hypothyroidism persist over time

Neonatal screening for congenital hypothyroidism in the Netherlands: Cognitive and motor outcome at 10 years of age

Contains fulltext : 35300.pdf (publisher's version ) (Open Access)CONTEXT: Patients with thyroidal congenital hypothyroidism (CH-T) born in The Netherlands in 1981-1982 showed persistent intellectual and motor deficits during childhood and adulthood, despite initiation of T(4) supplementation at a median age of 28 d after birth. OBJECTIVE: The present study examined whether advancement of treatment initiation to 20 d had resulted in improved cognitive and motor outcome. DESIGN/SETTING/PATIENTS: In 82 Dutch CH-T patients, born in 1992 to 1993 and treated at a median age of 20 d (mean, 22 d; range, 2-73 d), cognitive and motor outcome was assessed (mean age, 10.5 yr; range, 9.6-11.4 yr). Severity of CH-T was classified according to pretreatment free T(4) concentration. MAIN OUTCOME MEASURE: Cognitive and motor outcome of the 1992-1993 cohort in comparison to the 1981 to 1982 cohort was the main outcome measure. RESULTS: Patients with severe CH-T had lower full-scale (93.7), verbal (94.9), and performance (93.9) IQ scores than the normative population (P < 0.05), whereas IQ scores of patients with moderate and mild CH-T were comparable to those of the normative population. In all three severity subgroups, significant motor problems were observed, most pronounced in the severe CH-T group. No correlations were found between starting day of treatment and IQ or motor outcome. CONCLUSIONS: Essentially, findings from the 1992-1993 cohort were similar to those of the 1981-1982 cohort. Apparently, advancing initiation of T(4) supplementation from 28 to 20 d after birth did not result in improved cognitive or motor outcome in CH-T patients

Towards mathematical AI via a model of the content and process of mathematical question and answer dialogues

This paper outlines a strategy for building semantically meaningful representations and carrying out effective reasoning in technical knowledge domains such as mathematics. Our central assertion is that the semi-structured Q and A format, as used on the popular Stack Exchange network of websites, exposes domain knowledge in a form that is already reasonably close to the structured knowledge formats that computers can reason about. The knowledge in question is not only facts - but discursive, dialectical, argument for purposes of proof and pedagogy. We therefore assert that modelling the Q and A process computationally provides a route to domain understanding that is compatible with the day-to-day practices of mathematicians and students. This position is supported by a small case study that analyses one question from Mathoverflow in detail, using concepts from argumentation theory. A programme of future work, including a rigorous evaluation strategy, is then advanced

Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453