Planning and Proof Planning

. The paper adresses proof planning as a specific AI planning. It describes some peculiarities of proof planning and discusses some possible cross-fertilization of planning and proof planning. 1 Introduction Planning is an established area of Artificial Intelligence (AI) whereas proof planning introduced by Bundy in [2] still lives in its childhood. This means that the development of proof planning needs maturing impulses and the natural questions arise What can proof planning learn from its Big Brother planning?' and What are the specific characteristics of the proof planning domain that determine the answer?'. In turn for planning, the analysis of approaches points to a need of mature techniques for practical planning. Drummond [8], e.g., analyzed approaches with the conclusion that the success of Nonlin, SIPE, and O-Plan in practical planning can be attributed to hierarchical action expansion, the explicit representation of a plan's causal structure, and a very simple form of propo..

The Use of Proof Planning for Cooperative Theorem Proving

AbstractWe describebarnacle: a co-operative interface to theclaminductive theorem proving system. For the foreseeable future, there will be theorems which cannot be proved completely automatically, so the ability to allow human intervention is desirable; for this intervention to be productive the problem of orienting the user in the proof attempt must be overcome. There are many semi-automatic theorem provers: we call our style of theorem provingco-operative, in that the skills of both human and automaton are used each to their best advantage, and used together may find a proof where other methods fail. The co-operative nature of thebarnacleinterface is made possible by the proof planning technique underpinningclam. Our claim is that proof planning makes new kinds of user interaction possible.Proof planning is a technique for guiding the search for a proof in automatic theorem proving. Common patterns of reasoning in proofs are identified and represented computationally as proof plans, which can then be used to guide the search for proofs of new conjectures. We have harnessed the explanatory power of proof planning to enable the user to understand where the automatic prover got to and why it is stuck. A user can analyse the failed proof in terms ofclam's specification language, and hence override the prover to force or prevent the application of a tactic, or discover a proof patch. This patch might be to apply further rules or tactics to bridge the gap between the effects of previous tactics and the preconditions needed by a currently inapplicable tactic

Proof Planning

We describe proof planning, a technique for the global control of search in automatic theorem proving. A proof plan captures the common patterns of reasoning in a family of similar proofs and is used to guide the search for new proofs in this family. Proof plans are very similar to the plans constructed by plan formation techniques. Some differences are the non-persistence of objects in the mathematical domain, the absence of goal interaction in mathematics, the high degree of generality of proof plans, the use of a meta-logic to describe preconditions in proof planning and the use of annotations in formulae to guide search

Reasoned modelling critics: turning failed proofs into modelling guidance

The activities of formal modelling and reasoning are closely related. But while the rigour of building formal models brings significant benefits, formal reasoning remains a major barrier to the wider acceptance of formalism within design. Here we propose reasoned modelling critics — an approach which aims to abstract away from the complexities of low-level proof obligations, and provide high-level modelling guidance to designers when proofs fail. Inspired by proof planning critics, the technique combines proof-failure analysis with modelling heuristics. Here, we present the details of our proposal, implement them in a prototype and outline future plans

Optimal control with switches in the objective functional

This note offers a proof of the necessary conditions for optimal control problems that involve a finite number of discrete switches in the objective functional over the planning horizon.necessary conditions