15-815 Automated Theorem Proving

Handouts

Course material written by instructor.
Additional reading by other authors. Some are not publicly available and require a password.

ileanTAP, a Prolog implementation of a tableaux-based theorem prover for intuitionstic logic (see also Jens Otten).
Tabled logic programming, a technique for redundancy elimination in backward proof search (see also D.S. Warren, C.R. Ramakrishnan, and Terrance Swift).

The first line contains a complete set of notes in a single file. This is usually up-to-date. Note that I do not correct earlier handouts.

	Handout	PostScript	PDF	Date	Lectures
1-16	Automated Theorem Proving	atp.ps	atp.pdf	Nov 12	1-14, 18-24, 29-31
1	Natural Deduction	natded.ps	natded.pdf	Aug 23	1, 2
2	Proof Terms	pterms.ps	pterms.pdf	Aug 27	3
3	Intercalation	intercal.ps	intercal.pdf	Aug 30	4
4	Sequent Calculus	seq.ps	seq.pdf	Sep 1	5
5	Cut Elimination	cutelim.ps	cutelim.pdf	Sep 3	6
6	Proof Terms for Sequents	seqterms.ps	seqterms.pdf	Sep 10	7
7	Inversion Proofs	inversion.ps	inversion.pdf	Sep 13	8, 9
8	Focused Derivations	focus.ps	focus.pdf	Sep 16	10, 11
9	Residuating Equality	resid.ps	resid.pdf	Sep 20	12
10	Unification	unif.ps	unif.pdf	Sep 22	13
11	Properties of Unification	unif2.ps	unif2.pdf	Oct 6	14
12	Forward Sequent Calculus	fwdseq.ps	fwdseq.pdf	Oct 15	18
13	The Subformula Property	subform.ps	subform.pdf	Oct 18	19, 20
14	Inverse Focusing	invfocus.ps	invfocus.pdf	Oct 22	21
15	Resolution	resolution.ps	resolution.pdf	Oct 29	23, 24
16	Equality	equality.ps	equality.pdf	Nov 12	29, 30, 31

Anatoli Degtyarev, Grigori Mints, Tanel Tammet, and Andrei Voronkov. The inverse method. In Alan Robinson and Andrei Voronkov, editors, Handbook of Automated Reasoning. Elsevier Science Publishers, 1999. In preparation. Available electronically.
Tanel Tammet. A resolution theorem prover for intuitionistic logic. Draft manuscript, 1998. Available electronically.

W. Chen and D.S. Warren. Tabled evaluation with delaying for general logic programs. Journal of the ACM, 43(1):20-74, 1996.
Reiner Hähnle. Tableaux and related methods. In Alan Robinson and Andrei Voronkov, editors, Handbook of Automated Reasoning. Elsevier Science Publishers, 1999. In preparation. Available electronically.
Jens Otten and Christoph Kreitz. A connection based proof method for intuitionistic logic. In Proceedings of the 4th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods, pages 122-137. Springer Verlag LNAI 918, 1995. Available electronically.
Jens Otten and Christoph Kreitz. T-string-unification: Unifying prefixes in non-classical proof methods. In P. Miglioli, U. Moscato, D. Mundici, and M. Ornaghi, editors, Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods, pages 244-260. Springer Veralg LNAI 1071, 1996. Available electronically.
M. E. Stickel. A Prolog technology theorem prover. Theoretical Computer Science, 104(1):109-129, 1992.

I.V. Ramakrishnan, R. Sekar, and Andrei Voronkov. Term indexing. In Alan Robinson and Andrei Voronkov, editors, Handbook of Automated Reasoning. Elsevier Science Publishers, 1999. In preparation. Available electronically.

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