Notre Dame Journal of Formal Logic

Proof-finding Algorithms for Classical and Subclassical Propositional Logics

M. W. Bunder and R. M. Rizkalla

Abstract

The formulas-as-types isomorphism tells us that every proof and theorem, in the intuitionistic implicational logic $H_\rightarrow$, corresponds to a lambda term or combinator and its type. The algorithms of Bunder very efficiently find a lambda term inhabitant, if any, of any given type of $H_\rightarrow$ and of many of its subsystems. In most cases the search procedure has a simple bound based roughly on the length of the formula involved. Computer implementations of some of these procedures were done in Dekker. In this paper we extend these methods to full classical propositional logic as well as to its various subsystems. This extension has partly been implemented by Oostdijk.

Article information

Source
Notre Dame J. Formal Logic Volume 50, Number 3 (2009), 261-273.

Dates
First available: 10 November 2009

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1257862038

Digital Object Identifier
doi:10.1215/00294527-2009-011

Zentralblatt MATH identifier
05657219

Mathematical Reviews number (MathSciNet)
MR2572974

Subjects
Primary: 03B20: Subsystems of classical logic (including intuitionistic logic) 03B35: Mechanization of proofs and logical operations [See also 68T15] 03B40: Combinatory logic and lambda-calculus [See also 68N18] 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}

Keywords
proof-finding algorithms propositional logics

Citation

Bunder, M. W.; Rizkalla, R. M. Proof-finding Algorithms for Classical and Subclassical Propositional Logics. Notre Dame Journal of Formal Logic 50 (2009), no. 3, 261--273. doi:10.1215/00294527-2009-011. http://projecteuclid.org/euclid.ndjfl/1257862038.


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References

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