334 research outputs found

    Proof Plans for the Correction of False Conjectures

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    Theorem proving is the systematic derivation of a mathematical proof from a set of axioms by the use of rules of inference. We are interested in a related but far less explored problem: the analysis and correction of false conjectures, especially where that correction involves finding a collection of antecedents that, together with a set of axioms, transform non-theorems into theorems. Most failed search trees are huge, and special care is to be taken in order to tackle the combinatorial explosion phenomenon. Fortunately, the planning search space generated by proof plans, see [1], are moderately small. We have explored the possibility of using this technique in the implementation of an abduction mechanism to correct non-theorems

    Proof Plans for the Correction of False Conjectures

    Get PDF
    Theorem proving is the systematic derivation of a mathcmaticM proof from a set of axioms by the use of rules of inference. We ~re interested in a related but far less explored problem: the analysis and correction of false conjectures, especiMly where that correction involves finding a collection of antecedents that, together with a set of axioms, transform non-theorems into theorems. Most failed search trees are huge, and special care is to be taken in order to tackle the combinatorial explosion phenoraenom Fortunately, the planning search space generated by proof plans, see [1], are moderately small. We have explored the possibility of using this technique in the implementation of an abduction mechanism to correct non-theorems

    Discovering attacks on security protocols by refuting incorrect inductive conjectures

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    MATHsAiD: Automated Mathematical Theory Exploration

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    The aim of the MATHsAiD project is to build a tool for automated theorem-discovery; to design and build a tool to automatically conjecture and prove theorems (lemmas, corollaries, etc.) from a set of user-supplied axioms and definitions. No other input is required. This tool would, for instance, allow a mathematician to try several versions of a particular definition, and in a relatively small amount of time, be able to see some of the consequences, in terms of the resulting theorems, of each version. Moreover, the automatically discovered theorems could perhaps help the users to discover and prove further theorems for themselves. The tool could also easily be used by educators (to generate exercise sets, for instance) and by students as well. In a similar fashion, it might also prove useful in enabling automated theorem provers to dispatch many of the more difficult proof obligations arising in software verification, by automatically generating lemmas which are needed by the prover, in order to finish these proofs

    Constructing Induction Rules for Deductive Synthesis Proofs

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    We describe novel computational techniques for constructing induction rules for deductive synthesis proofs. Deductive synthesis holds out the promise of automated construction of correct computer programs from specifications of their desired behaviour. Synthesis of programs with iteration or recursion requires inductive proof, but standard techniques for the construction of appropriate induction rules are restricted to recycling the recursive structure of the specifications. What is needed is induction rule construction techniques that can introduce novel recursive structures. We show that a combination of rippling and the use of meta-variables as a least-commitment device can provide such novelty. Key words: deductive synthesis, proof planning, induction, theorem proving, middle-out reasoning.

    Strategic Issues, Problems and Challenges in Inductive Theorem Proving

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    Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP
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