10,711 research outputs found
The use of data-mining for the automatic formation of tactics
This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques
Finding and using analogies to guide mathematical proof
This thesis is concerned with reasoning by analogy within the context of auto-mated problem solving. In particular, we consider the provision of an analogical reasoning component to a resolution theorem proving system. The framework for reasoning by analogy which we use (called Basic APS) contains three major components -the finding of analogies (analogy matching), the construction of analogical plans, and the application of the plans to guide the search of a theorem prover. We first discuss the relationship of analogy to other machine learning techniques. We then develop programs for each of the component processes of Basic APS.First we consider analogy matching. We reconstruct, analyse and crticise two previous analogy matchers. We introduce the notion of analogy heuristics in order to understand the matchers. We find that we can explain the short-comings of the matchers in terms of analogy heuristics. We then develop a new analogy matching algorithm, based on flexible application of analogy heuristics, and demonstrate its superiority to the previous matchers.We go on to consider analogical plan construction. We describe procedures for constructing a plan for the solution of a problem, given the solution of a different problem and an analogy match between the two problems. Again, we compare our procedures with corresponding ones from previous systems.We then describe procedures for the execution of analogical plans. We demon-strate the procedures on a number of example analogies. The analogies involved are straightforward for a human, but the problems themselves involve.huge search spaees, if tackled directly using resolution. By comparison with unguided search, we demonstrate the dramatic reductfon in search entaile_d by the use of an ana-logical plan.We then consider some directions for development of our analogy systems, which have not yet been implemented. Firstly, towards more flexible and power-ful execution of analogical plans. Secondly, towards an analogy system which can improve its own ability to find and apply analogies over the course of experience
Decision-making and problem-solving methods in automation technology
The state of the art in the automation of decision making and problem solving is reviewed. The information upon which the report is based was derived from literature searches, visits to university and government laboratories performing basic research in the area, and a 1980 Langley Research Center sponsored conferences on the subject. It is the contention of the authors that the technology in this area is being generated by research primarily in the three disciplines of Artificial Intelligence, Control Theory, and Operations Research. Under the assumption that the state of the art in decision making and problem solving is reflected in the problems being solved, specific problems and methods of their solution are often discussed to elucidate particular aspects of the subject. Synopses of the following major topic areas comprise most of the report: (1) detection and recognition; (2) planning; and scheduling; (3) learning; (4) theorem proving; (5) distributed systems; (6) knowledge bases; (7) search; (8) heuristics; and (9) evolutionary programming
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
Abstract Canonical Inference
An abstract framework of canonical inference is used to explore how different
proof orderings induce different variants of saturation and completeness.
Notions like completion, paramodulation, saturation, redundancy elimination,
and rewrite-system reduction are connected to proof orderings. Fairness of
deductive mechanisms is defined in terms of proof orderings, distinguishing
between (ordinary) "fairness," which yields completeness, and "uniform
fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi
Validating specifications of dynamic systems using automated reasoning techniques
In this paper, we propose a new approach to validating formal specifications of observable behavior of discrete dynamic systems. By observable behavior we mean system behavior as observed by users or other systems in the environment of the system. Validation of a formal specification of an informal domain tries to answer the question whether the specification actually describes the intended domain. This differs from the verification problem, which deals with the correspondence between formal objects, e.g. between a formal specification of a system and an implementation of it. We consider formal specifications of object-oriented dynamic systems that are subject to static and dynamic integrity constraints. To validate that such a specification expresses the intended behavior, we propose to use a tool that can answer reachability queries. In a reachability query we ask whether the system can evolve from one state into another without violating the integrity constraints. If the query is answered positively, the system should exhibit an example path between the states; if the answer is negative, the system should explain why this is so. An example path produced by the tool can be used to produce scenarios for presentations of system behavior, but can also be used as a basis for acceptance testing. In this paper, we discuss the use of planning and theoremproving techniques to answer such queries, and illustrate the use of reachability queries in the context of information system development
Constructing Conditional Plans by a Theorem-Prover
The research on conditional planning rejects the assumptions that there is no
uncertainty or incompleteness of knowledge with respect to the state and
changes of the system the plans operate on. Without these assumptions the
sequences of operations that achieve the goals depend on the initial state and
the outcomes of nondeterministic changes in the system. This setting raises the
questions of how to represent the plans and how to perform plan search. The
answers are quite different from those in the simpler classical framework. In
this paper, we approach conditional planning from a new viewpoint that is
motivated by the use of satisfiability algorithms in classical planning.
Translating conditional planning to formulae in the propositional logic is not
feasible because of inherent computational limitations. Instead, we translate
conditional planning to quantified Boolean formulae. We discuss three
formalizations of conditional planning as quantified Boolean formulae, and
present experimental results obtained with a theorem-prover
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