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On the strength of proof-irrelevant type theories

Benjamin Werner, Shankar Natarajan
2008 Logical Methods in Computer Science  
We present a type theory with some proof-irrelevance built into the conversion rule.  ...  We show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of equality, that is, almost classical logic.  ...  In other words, a proof-system built upon a theory as the one presented here would allow the user to eciently exploit the computational behavior of a constructive proof in order to prove new facts.  ... 
doi:10.2168/lmcs-4(3:13)2008 fatcat:5hzx7dhn25efnnej4muo54oumy

On the Proof Theory of Regular Fixed Points [chapter]

David Baelde
2009 Lecture Notes in Computer Science  
We provide a coinductive characterization of inclusion that yields a natural bridge to proof-theory.  ...  This leads us to generalize these observations to regular formulas, obtaining new insights about inductive theorem proving and cyclic proofs in particular.  ...  While the finite behavior case is trivially handled in the proof-theory of such logics, finite-state behaviors are not so well understood.  ... 
doi:10.1007/978-3-642-02716-1_8 fatcat:5iou2rnduvh3jnfwwpowzf2jpe

On the Strength of Proof-Irrelevant Type Theories [chapter]

Benjamin Werner
2006 Lecture Notes in Computer Science  
We present a type theory with some proof-irrelevance built into the conversion rule.  ...  Finally we show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of equality, that is, almost classical logic.  ...  In other words, a proof-system built upon a theory as the one presented here would allow the user to eciently exploit the computational behavior of a constructive proof in order to prove new facts.  ... 
doi:10.1007/11814771_49 fatcat:wi45amls7fbabpqxloqkwzlurq

Why Proof-Theory Matters in Specification-Based Testing

Alberto Momigliano
2020 Italian Conference on Theoretical Computer Science  
We survey some recent developments in giving a logical reconstruction of specification-based testing via the lenses of structural proof-theory.  ...  SBT as Proof-Search We use as a running examples a call-by-value λ-calculus (where values are lambdas and numerals) whose static and big-step dynamic semantics follows -readers should  ...  Acknowledgment A shout-out to my co-authors in this line of work: Rob Blanco, James Cheney, Francesco Komauli, Dale Miller and Matteo Pessina.  ... 
dblp:conf/ictcs/Momigliano20 fatcat:bkji3bx47bggfeahzzsotsvy4q

A 'Theory' Mechanism for a Proof-Verifier Based on First-Order Set Theory [chapter]

Eugenio G. Omodeo, Jacob T. Schwartz
2002 Lecture Notes in Computer Science  
Through several examples, centered on the finite summation operation, we illustrate the potential utility in large-scale proof-development of the 'theory' mechanism: utility which stems in part from the  ...  We propose classical set theory as the core of an automated proof-verifier and outline a version of it, designed to assist in proof development, which is indefinitely expansible with function symbols generated  ...  Acknowledgements We thank Ernst-Erich Doberkat (Universität Dortmund, D), who brought to our attention the text by Frege cited in the epigraph of this paper.  ... 
doi:10.1007/3-540-45632-5_9 fatcat:c2a2sn43krf3vg3qyeizzpuy5i

The Complete Proof Theory of Hybrid Systems

Andre Platzer
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science  
We now show that, proof-theoretically, this is not the case. We present a complete proof-theoretical alignment that interreduces the discrete dynamics and the continuous dynamics of hybrid systems.  ...  This fundamental cornerstone sheds light on the nature of hybridness and enables flexible and provably perfect combinations of discrete reasoning with continuous reasoning that lift to all aspects of hybrid  ...  On top of its theoretical value and the full provability alignment that our new result shows, our discrete completeness result is significant in that-in computer science and verification-programs are closer  ... 
doi:10.1109/lics.2012.64 dblp:conf/lics/Platzer12a fatcat:rylkaeazdbc3dizsyfaziliu54

Some Observations on the Proof Theory of Second Order Propositional Multiplicative Linear Logic [chapter]

Lutz Straßburger
2009 Lecture Notes in Computer Science  
On the technical level this paper provides two new aspects of the proof theory of MLL2 with units. First, we give a novel proof system in the framework of the calculus of structures.  ...  The main feature of the new system is the consequent use of deep inference, which allows us to observe a decomposition which is a version of Herbrand's theorem that is not visible in the sequent calculus  ...  Introduction The question of when two proofs are the same is important for proof theory and its applications.  ... 
doi:10.1007/978-3-642-02273-9_23 fatcat:eedkybm3ifhczahnbujzsannaq

Theorem Proving Based on Proof Scores for Rewrite Theory Specifications of OTSs [chapter]

Kazuhiro Ogata, Kokichi Futatsugi
2014 Lecture Notes in Computer Science  
. … • Equational theory specification: Inductive proof with search (1) 8 … t t t c C 1 C 2 C n Let SPEC-T be a specification (module) in which there exists exactly one trans rule whose label is t and c  ...  2011, SAS 2014] • Suggesting theorem proving that rewrite theory specifications enjoy invariant properties by writing proof scores in CafeOBJ • An authentication protocol is used to describe it  ...  Summary • NSLPK has been used to demonstrate that (some specific style/class of) rewrite theory specifications can be used for theorem proving based on proof scores.  ... 
doi:10.1007/978-3-642-54624-2_31 fatcat:tssyw3urfbggrhutd2xfu44dgy

On the Convergence of Reduction-based and Model-based Methods in Proof Theory

Gilles Dowek
2008 Electronical Notes in Theoretical Computer Science  
In the recent past, the reduction-based and the model-based methods to prove cut elimination have converged, so that they now appear just as two sides of the same coin.  ...  Then, a simple induction on proof structure shows that, in constructive natural deduction, the last rule of a cut free proof in the empty theory is an introduction.  ...  to extract programs from such proofs, rely on cut elimination theorems, asserting that when a proposition is provable in some theory, it has a proof of a special form: a cut free proof.  ... 
doi:10.1016/j.entcs.2008.03.070 fatcat:wjnikmrmobasbns5lx4wdpyhjm

On linear rewriting systems for Boolean logic and some applications to proof theory

Anupam Das, Lutz Strassburger, Maribel Fernandez
2017 Logical Methods in Computer Science  
Linear rules have played an increasing role in structural proof theory in recent years.  ...  We draw tools and concepts from term rewriting, Boolean function theory and graph theory in order to access some required intermediate results.  ...  We would like to thank Paola Bruscoli, Kaustuv Chaudhuri, Alessio Guglielmi, Willem Heijltjes and others in the deep inference community for many fruitful discussions on these topics.  ... 
doi:10.2168/lmcs-12(4:9)2016 fatcat:q52wxqmhvzcidg2jm76mq5qc24

Proofs by induction in equational theories with constructors

Gerard Huet, Jean-Marie Hullot
1980 21st Annual Symposium on Foundations of Computer Science (sfcs 1980)  
The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.  ...  HAL Id: inria-00076533 https://hal.inria.fr/inria-00076533 Submitted on 24 May 2006 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents,  ... 
doi:10.1109/sfcs.1980.37 dblp:conf/focs/HuetH80 fatcat:pgky2s3itjdctcldbokbyg3tye

On the Continuity of Gelfond-Lifschitz Operator and Other Applications of Proof-Theory in ASP [chapter]

V. W. Marek, J. B. Remmel
2008 Lecture Notes in Computer Science  
The introduction of the formula rΦP leads to a double-backtracking algorithm for computation of stable models by reduction to satisfiability of suitably chosen propositional theories.  ...  This algorithm does not use the reduction via loop-formulas as proposed in [LZ02] or its extension proposed in [FLL06].  ...  The P -proof schemes described in this paper represent one possible candidate of such a proof system for ASP.  ... 
doi:10.1007/978-3-540-89982-2_25 fatcat:wjpyvtauo5hlflwqwy5cdm45bq

A special issue on structural proof theory, automated reasoning and computation in celebration of Dale Miller's 60th birthday

David Baelde, Amy Felty, Gopalan Nadathur, Alexis Saurin
2019 Mathematical Structures in Computer Science  
proof theory and its application to computation and reasoning.  ...  The genesis of this special issue was in a meeting that took place at Université Paris Diderot on December 15 and 16, 2016.  ...  proof theory and its application to computation and reasoning.  ... 
doi:10.1017/s0960129519000136 fatcat:tjt7lfkumfc3hgum6h77yjapnu

Proof Theory for Kleene Algebra

C. Hardin
20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)  
We develop an (infinitary) proof system, based on well-founded trees of finite automata, which is sound and complete for this theory.  ...  A small modification of this system yields a proof system which is sound and complete for the universal Horn theory of * -continuous Kleene algebras with tests (KAT * ).  ...  Introduction Kleene algebra (KA) arises in many areas of computer science, such as automata theory, the design and analysis of algorithms, dynamic logic, and program semantics.  ... 
doi:10.1109/lics.2005.37 dblp:conf/lics/Hardin05 fatcat:3nbvimxbgzbybbefjpcb3lj5ga

Intensionality, extensionality, and proof irrelevance in modal type theory

F. Pfenning
Proceedings 16th Annual IEEE Symposium on Logic in Computer Science  
We develop a uniform type theory that integrates intensionality, extensionality, and proof irrelevance as judgmental concepts.  ...  Our type theory contrasts with previous approaches that a priori distinguish propositions (whose proofs are all identified-only their existence is important) from specifications (whose implementations  ...  If our operational interpretation of type theory is based on staged computation [DP00] , then the modality is necessary to reason about staged programs.  ... 
doi:10.1109/lics.2001.932499 dblp:conf/lics/Pfenning01 fatcat:7ki2zmyxwbfa7fvnuhe4qetgge
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