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Proof Theory
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The article was published on 1975-01-01 and is currently open access. It has received 770 citations till now. The article focuses on the topics: Proof theory & Gentzen's consistency proof.read more
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Journal ArticleDOI
Unsound inferences make proofs shorter
Juan P. Aguilera,Matthias Baaz +1 more
TL;DR: The authors give examples of calculi that extend Gentzen's sequent calculus LK by unsound quantifier inferences in such a way that derivations lead only to true sequents, and proofs therein are nonelementarily shorter than LK-proofs.
Book ChapterDOI
Methods of automated reasoning
TL;DR: Classical deductive methods for first-order logic like resolution and the connection method are introduced as a derived form of natural deduction for performing inferences in this chapter.
Dissertation
Second-order logic : ontological and epistemological problems
Abstract: In this thesis I provide a survey over different approaches to second-order logic and its interpretation, and introduce a novel approach. Of special interest are the questions whether (a particular form of) second-order logic can count as logic in some (further to be specified) proper sense of logic, and what epistemic status it occupies. More specifically, second-order logic is sometimes taken to be mathematical, a mere notational variant of some fragment of set theory. If this is the case, it might be argued that it does not have the “epistemic innocence” which would be needed for, e.g., foundational programmes in (the philosophy of) mathematics for which second-order logic is sometimes used. I suggest a Deductivist conception of logic, that characterises logical consequence by means of inference rules, and argue that on this conception second-order logic should count as logic in the proper sense.
Journal ArticleDOI
Bounded linear-time temporal logic: A proof-theoretic investigation
TL;DR: The completeness theorems for BLTL and FBLTL are proved for simple semantics with both a bounded time domain and some bounded valuation conditions on temporal operators and its monadic fragment is shown to be decidable.
Book ChapterDOI
The Semantic Tableaux Version of the Second Incompleteness Theorem Extends Almost to Robinson's Arithmetic Q
TL;DR: The Second Incompleteness Theorem is generalized almost to the level of Robinson’s System Q, such that if α is any finite consistent extension of Q +V then α will be unable to prove its Semantic Tableaux consistency.