Deductive synthesis of recursive plans in linear logic

Centre for Intelligent Systems and their ApplicationsConventionally, the problem of plan formation in Artificial Intelligence deals with the generation of plans in the form of a sequence of actions. This thesis describes an approach to extending the expressiveness of plans to include conditional branches and recursion. This allows problems to be solved at a higher level, such that a single plan in such a language is capable of solving a class of problems rather than a single problem instance. A plan of fixed size may solve arbitrarily large problem instances. To form such plans, we take a deductive planning approach, in which the formation of the plan goes hand-in-hand with the construction of the proof that the plan specification is realisable. The formalism used here for specifying and reasoning with planning problems is Girard's Institutionistic Linear Logic (ILL), which is attractive for planning problems because state change can be expressed directly as linear implication, with no need for frame axioms. We extract plans by means of the relationship between proofs in ILL and programs in the style of Abramsky. We extend the ILL proof rules to account for induction over inductively defined types, thereby allowing recursive plans to be synthesised. We also adapt Abramsky's framework to partially evaluate and execute the plans in the extended language. We give a proof search algorithm tailored towards the fragment of the ILL employed (excluding induction rule selection). A system implementation, Lino, comprises modules for proof checking, automated proof search, plan extraction and partial evaluation of plans. We demonstrate the encodings and solutions in our framework of various planning domains involving recursion. We compare the capabilities of our approach with the previous approaches of Manna and Waldinger, Ghassem-Sani and Steel, and Stephen and Biundo. We claim that our approach gives a good balance between coverage of problems that can be described and the tractability of proof search

Tools and techniques for machine-assisted meta-theory

Machine-assisted formal proofs are becoming commonplace in certain fields of mathematics and theoretical computer science. New formal systems and variations on old ones are constantly invented. The meta-theory of such systems, i.e. proofs about the system as opposed to proofs within the system, are mostly done informally with a pen and paper. Yet the meta-theory of deductive systems is an area which would obviously benefit from machine support for formal proof. Is the software currently available sufficiently powerful yet easy enough to use to make machine assistance for formal meta-theory a viable proposition? This thesis presents work done by the author on formalizing proof theory from [DP97a] in various formal systems: SEQUEL [Tar93, Tar97], Isabelle [Pau94] and Coq [BB+96]. SEQUEL and Isabelle were found to be difficult to use for this type of work. In particular, the lack of automated production of induction principles in SEQUEL and Isabelle undermined confidence in the resulting formal proofs. Coq was found to be suitable for the formalisation methodology first chosen: the use of nameless dummy variables (de Bruijn indices) as pioneered in [dB72]. A second approach (inspired by the work of McKinna and Pollack [vBJMR94, MP97]) formalising named variables was also the subject of some initial work, and a comparison of these two approaches is presented. The formalisation was restricted to the implicational fragment of propositional logic. The informal theory has been extended to cover full propositional logic by Dyckhoff and Pinto, and extension of the formalisation using de Bruijn indices would appear to present few difficulties. An overview of other work in this area, in terms of both the tools and formalisation methods, is also presented. The theory formalised differs from other such work in that other formalisations have involved only one calculus. [DP97a] involves the relationships between three different calculi. There is consequently a much greater requirement for equality reasoning in the formalisation. It is concluded that a formalisation of any significance is still difficult, particularly one involving multiple calculi. No tools currently exist that allow for the easy representation of even quite simple systems in a way that fits human intuitions while still allowing for automatic derivation of induction principles. New work on integrating higher order abstract syntax and induction may be the way forward, although such work is still in the early stages

2008-2009 Undergraduate Bulletin

https://soundideas.pugetsound.edu/bulletins/1009/thumbnail.jp

2010-2011 Undergraduate Bulletin

https://soundideas.pugetsound.edu/bulletins/1011/thumbnail.jp

2009-2010 Undergraduate Bulletin

https://soundideas.pugetsound.edu/bulletins/1010/thumbnail.jp

General Catalog 1994-1996

Contains course descriptions, University college calendar, and college administration.https://digitalcommons.usu.edu/universitycatalogs/1038/thumbnail.jp

2011-2012 Undergraduate Bulletin

https://soundideas.pugetsound.edu/bulletins/1012/thumbnail.jp

Undergraduate Catalogue 2015-2017

https://digitalscholarship.tnstate.edu/undergraduatecatalogues/1001/thumbnail.jp

Undergraduate Catalogue 2017-2019

https://digitalscholarship.tnstate.edu/undergraduatecatalogues/1000/thumbnail.jp