8,817 research outputs found
Learning to Prove Theorems via Interacting with Proof Assistants
Humans prove theorems by relying on substantial high-level reasoning and
problem-specific insights. Proof assistants offer a formalism that resembles
human mathematical reasoning, representing theorems in higher-order logic and
proofs as high-level tactics. However, human experts have to construct proofs
manually by entering tactics into the proof assistant. In this paper, we study
the problem of using machine learning to automate the interaction with proof
assistants. We construct CoqGym, a large-scale dataset and learning environment
containing 71K human-written proofs from 123 projects developed with the Coq
proof assistant. We develop ASTactic, a deep learning-based model that
generates tactics as programs in the form of abstract syntax trees (ASTs).
Experiments show that ASTactic trained on CoqGym can generate effective tactics
and can be used to prove new theorems not previously provable by automated
methods. Code is available at https://github.com/princeton-vl/CoqGym.Comment: Accepted to ICML 201
Rational coordination of crowdsourced resources for geo-temporal request satisfaction
Existing mobile devices roaming around the mobility field should be considered as useful resources in geo-temporal request satisfaction. We refer to the capability of an application to access a physical device at particular geographical locations and times as GeoPresence, and we pre- sume that mobile agents participating in GeoPresence-capable applica- tions should be rational, competitive, and willing to deviate from their routes if given the right incentive. In this paper, we define the Hitch- hiking problem, which is that of finding the optimal assignment of re- quests with specific spatio-temporal characteristics to competitive mobile agents subject to spatio-temporal constraints. We design a mechanism that takes into consideration the rationality of the agents for request sat- isfaction, with an objective to maximize the total profit of the system. We analytically prove the mechanism to be convergent with a profit com- parable to that of a 1/2-approximation greedy algorithm, and evaluate its consideration of rationality experimentally.Supported in part by NSF Grants; #1430145, #1414119, #1347522, #1239021, and #1012798
Rational physical agent reasoning beyond logic
The paper addresses the problem of defining a theoretical physical agent framework that satisfies practical requirements of programmability by non-programmer engineers and at the same time permitting fast realtime operation of agents on digital computer networks. The objective of the new framework is to enable the satisfaction of performance requirements on autonomous vehicles and robots in space exploration, deep underwater exploration, defense reconnaissance, automated manufacturing and household automation
Mechanism design for spatio-temporal request satisfaction in mobile networks
Mobile agents participating in geo-presence-capable crowdsourcing applications should be presumed rational, competitive, and willing to deviate from their routes if given the right incentive. In this paper, we design a mechanism that takes into consideration this rationality for request satisfaction in such applications. We propose the Geo-temporal Request Satisfaction (GRS) problem to be that of finding the optimal assignment of requests with specific spatio-temporal characteristics to competitive mobile agents subject to spatio-temporal constraints. The objective of the GRS problem is to maximize the total profit of the system subject to our rationality assumptions. We define the problem formally, prove that it is NP-Complete, and present a practical solution mechanism, which we prove to be convergent, and which we evaluate experimentally.National Science Foundation (1012798, 0952145, 0820138, 0720604, 0735974
Improving QED-Tutrix by Automating the Generation of Proofs
The idea of assisting teachers with technological tools is not new.
Mathematics in general, and geometry in particular, provide interesting
challenges when developing educative softwares, both in the education and
computer science aspects. QED-Tutrix is an intelligent tutor for geometry
offering an interface to help high school students in the resolution of
demonstration problems. It focuses on specific goals: 1) to allow the student
to freely explore the problem and its figure, 2) to accept proofs elements in
any order, 3) to handle a variety of proofs, which can be customized by the
teacher, and 4) to be able to help the student at any step of the resolution of
the problem, if the need arises. The software is also independent from the
intervention of the teacher. QED-Tutrix offers an interesting approach to
geometry education, but is currently crippled by the lengthiness of the process
of implementing new problems, a task that must still be done manually.
Therefore, one of the main focuses of the QED-Tutrix' research team is to ease
the implementation of new problems, by automating the tedious step of finding
all possible proofs for a given problem. This automation must follow
fundamental constraints in order to create problems compatible with QED-Tutrix:
1) readability of the proofs, 2) accessibility at a high school level, and 3)
possibility for the teacher to modify the parameters defining the
"acceptability" of a proof. We present in this paper the result of our
preliminary exploration of possible avenues for this task. Automated theorem
proving in geometry is a widely studied subject, and various provers exist.
However, our constraints are quite specific and some adaptation would be
required to use an existing prover. We have therefore implemented a prototype
of automated prover to suit our needs. The future goal is to compare
performances and usability in our specific use-case between the existing
provers and our implementation.Comment: In Proceedings ThEdu'17, arXiv:1803.0072
A Mechanism for Fair Distribution of Resources without Payments
We design a mechanism for Fair and Efficient Distribution of Resources
(FEDoR) in the presence of strategic agents. We consider a multiple-instances,
Bayesian setting, where in each round the preference of an agent over the set
of resources is a private information. We assume that in each of r rounds n
agents are competing for k non-identical indivisible goods, (n > k). In each
round the strategic agents declare how much they value receiving any of the
goods in the specific round. The agent declaring the highest valuation receives
the good with the highest value, the agent with the second highest valuation
receives the second highest valued good, etc. Hence we assume a decision
function that assigns goods to agents based on their valuations. The novelty of
the mechanism is that no payment scheme is required to achieve truthfulness in
a setting with rational/strategic agents. The FEDoR mechanism takes advantage
of the repeated nature of the framework, and through a statistical test is able
to punish the misreporting agents and be fair, truthful, and socially
efficient. FEDoR is fair in the sense that, in expectation over the course of
the rounds, all agents will receive the same good the same amount of times.
FEDoR is an eligible candidate for applications that require fair distribution
of resources over time. For example, equal share of bandwidth for nodes through
the same point of access. But further on, FEDoR can be applied in less trivial
settings like sponsored search, where payment is necessary and can be given in
the form of a flat participation fee. To this extent we perform a comparison
with traditional mechanisms applied to sponsored search, presenting the
advantage of FEDoR
A Logic-based Approach for Recognizing Textual Entailment Supported by Ontological Background Knowledge
We present the architecture and the evaluation of a new system for
recognizing textual entailment (RTE). In RTE we want to identify automatically
the type of a logical relation between two input texts. In particular, we are
interested in proving the existence of an entailment between them. We conceive
our system as a modular environment allowing for a high-coverage syntactic and
semantic text analysis combined with logical inference. For the syntactic and
semantic analysis we combine a deep semantic analysis with a shallow one
supported by statistical models in order to increase the quality and the
accuracy of results. For RTE we use logical inference of first-order employing
model-theoretic techniques and automated reasoning tools. The inference is
supported with problem-relevant background knowledge extracted automatically
and on demand from external sources like, e.g., WordNet, YAGO, and OpenCyc, or
other, more experimental sources with, e.g., manually defined presupposition
resolutions, or with axiomatized general and common sense knowledge. The
results show that fine-grained and consistent knowledge coming from diverse
sources is a necessary condition determining the correctness and traceability
of results.Comment: 25 pages, 10 figure
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