Formalization of the fundamental group in untyped set theory using auto2

We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.Comment: 17 pages, accepted for ITP 201

Learning-assisted Theorem Proving with Millions of Lemmas

Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck.Comment: journal version of arXiv:1310.2797 (which was submitted to LPAR conference

A simplified framework for first-order languages and its formalization in Mizar

A strictly formal, set-theoretical treatment of classical first-order logic is given. Since this is done with the goal of a concrete Mizar formalization of basic results (Lindenbaum lemma; Henkin, satisfiability, completeness and Lowenheim-Skolem theorems) in mind, it turns into a systematic pursue of simplification: we give up the notions of free occurrence, of derivation tree, and study what inference rules are strictly needed to prove the mentioned results. Afterwards, we discuss details of the actual Mizar implementation, and give general techniques developed therein.Comment: Ph.D. thesis, defended on January, 20th, 201

An Investigation of Area Speed Flow Relationships by Micro-Simulation Single Links

This working paper is the first in a series relating to the EPSRC funded project, " The Definition of Capacity in Urban Road Networks : The role of Area Speed-Flow Relationships". It defines the measures collected and the methods for data collection in terms of space-time diagrams. The four measures are collected by simulating different levels of demand. Two cases are presented, the first simulates constant demand throughout each simulation period, the second simulates a demand profile which stays uniform as peak demand increases. The paper concentrates on single link models with only one OD pair and only one route. Two equivalent networks are presented. The first represents a single link where the capacity of the link is maintained. The second is a purely hypothetical network where the capacity is reduced to zero as demand increases. This is achieved by a loop configuration so that the departure rate is affected by the queue blocking-back on itself

D4.6 Report on the results of cycle 3 demonstrators:Aggregates internal deliverables ID4.12, ID4.13, ID4.14, ID4.15, ID4.16

Hernández-Leo, D., Sligte, H., Glahn, C., Krekels, B., Keuls, C., Louys, A., Stefanov, K., Perez, M., Chacón, J., Santos, P., Mazzetti, A., Herder, E., Maxwell, K., Kiercheben, J., Griffiths, D., & Kluijfhout, E. (2009). D4.6 - Report on the results of cycle 3 demonstrators. Aggregates internal deliverables ID4.12, ID4.13, ID4.14, ID4.15, ID4.16. TENCompetence.This document includes the evaluation results of the Cycle 3 real-life evaluation activities. A cross-analysis of the results is compiled in order to present the impact indicators of the project in terms of outreach, learning benefits, organizational implications, and business opportunities identified in these experiences. The implementations and eight business/market-relevant demonstrators conducted in collaboration with external "adopter organizations" from different countries in Europe. These external organizations are Associated Partners or different units within the partners'organization. The revised pilots and the demonstrators test the tooling achieved along DIP-3. Both pilots and business demonstrators show to provide benefits to socially- and industrially-relevant scenarios. Areas of proven special impact include adult competence developmentfor social inclusion, provision of learning paths to support competence development of distributed professionals, informal competence development, human resources personal competence development, and sharing of competence profiles between organizations to support the mobility of their professionals.The work on this publication has been sponsored by the TENCompetence Integrated Project that is funded by the European Commission's 6th Framework Programme, priority IST/Technology Enhanced Learning. Contract 027087 [http://www.tencompetence.org