Results 1 to 10 of about 12,179 (98)
Reverse mathematics and well-ordering principles [PDF]
, 2011 The paper is concerned with generally Pi^1_2 sentences of the form 'if X is well ordered then f(X) is well ordered', where f is a standard proof theoretic function from ordinals to ordinals.
Rathjen, Michael, Weiermann, Andreas
core +1 more source
Proof Theory of Finite-valued Logics [PDF]
, 1993 The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux
Zach, Richard
core +5 more sources
Normalisation Control in Deep Inference via Atomic Flows [PDF]
, 2008 We introduce `atomic flows': they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations. This allows us to
Alessio Guglielmi +2 more
core +8 more sources
The Epsilon Calculus and Herbrand Complexity [PDF]
, 2005 Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which ...
A. Blass +20 more
core +2 more sources
Refinement Types for Logical Frameworks and Their Interpretation as Proof Irrelevance [PDF]
, 2010 Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical forms are ...
David Aspinall and Adriana B. Compagnoni +10 more
core +8 more sources
Dual-Context Calculi for Modal Logic [PDF]
, 2020 We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of assumptions, one of which
Kavvos, G. A.
core +4 more sources
Cut-Simulation and Impredicativity [PDF]
, 2009 We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for classical type ...
Benzmueller, Christoph +2 more
core +2 more sources
Elimination of Cuts in First-order Finite-valued Logics [PDF]
, 1993 A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established.
Baaz, Matthias +2 more
core +4 more sources
The Sequent Calculus of Skew Monoidal Categories [PDF]
, 2018 International ...
Uustalu, Tarmo +2 more
core +4 more sources
Systematic construction of natural deduction systems for many-valued logics [PDF]
, 1993 A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables
Baaz, Matthias +2 more
core +2 more sources