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Proof Theory of Finite-valued Logics
The main aim of this report is to develop the proof theory of finite-valued first order logics in a general way, and to present some of the more important results in this area. Expand
Systematic construction of natural deduction systems for many-valued logics
A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited and soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems fornatural deduction systems. Expand
Hypersequent and the Proof Theory of Intuitionistic Fuzzy Logic
It is shown that the system is sound and complete, and allows cut-elimination, and a question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively. Expand
Compact propositional Godel logics
  • M. Baaz, R. Zach
  • Computer Science, Mathematics
  • Proceedings. 28th IEEE International Symposium…
  • 27 May 1998
It is shown that there is a rich structure of infinite-valued Godel logics, only one of which is compact, and that the compact infinite- valued Godel logic is the only one which interpolates, and the onlyOne with an r.e. entailment relation. Expand
Vagueness, Logic and Use: Four Experimental Studies on Vagueness
Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is BoniniExpand
Elimination of Cuts in First-order Finite-valued Logics
A uniform construction for sequent calculi for finite-valued first-order logics with dis- tribution quantifiers is exhibited and an analog of Herbrand's theorem for the four-valued knowledge- representation logic of Belnap and Ginsberg is presented. Expand
The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program
  • R. Zach
  • Mathematics, Computer Science
  • Synthese
  • 24 February 2001
The paper traces the development of the ``simultaneous development of logic and mathematics'' through the ∈-notation and provides an analysis of Ackermann's consistency proofs for primitive recursive arithmetic and for the first comprehensive mathematical system, the latter using thesubstitution method. Expand
Hilbert's program then and now
Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,”Expand
Dual systems of sequents and tableaux for many-valued logics
Matthias Baaz Christian G. Fermuller Richard ZachNovember 25, 1992Technical Report TUW{E185.2{BFZ.2{921993 Workshop on Theorem Proving withAnalytic TableauxTechnische Universitat WienInstitut furExpand