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On Strong Normalization in Proof-Graphs for Propositional Logic

2016
*
Electronical Notes in Theoretical Computer Science
*

*In*

*proof*-

*graphs*, the main reason

*for*obtaining the

*strong*

*normalization*property using such simple complexity measure is a direct consequence of the fact that each formula occurs only once

*in*the

*proof*-

*graph*...

*In*this work, we consider full minimal

*propositional*

*logic*and show how to reduce (eliminating maximal formulas) these representations such that

*strong*

*normalization*theorem can be proved by simply counting ...

*Proof*-

*graphs*

*for*full

*propositional*

*logic*

*In*[6] we considered implication as the only

*logic*connective. ...

##
###
Proof-graphs for Minimal Implicational Logic

2014
*
Electronic Proceedings in Theoretical Computer Science
*

*In*the present paper we give a precise definition of

*proof*-

*graphs*

*for*the minimal implicational

*logic*, together with a

*normalization*procedure

*for*these

*proof*-

*graphs*. ... We present the formalism of

*proof*-

*graphs*

*for*purely implicational

*logic*, which are

*graphs*of a specific shape that are intended to capture the

*logical*structure of a deduction. ... [1] , that use

*graphs*

*for*representing

*proofs*, pointing out that

*proof*-

*graphs*offer a better way to facilitate the visualisation and understanding of

*proofs*

*in*the underlying

*logic*. ...

##
###
Basic proof theory

1998
*
Science of Computer Programming
*

Second-order

doi:10.1016/s0167-6423(98)00002-1
fatcat:zaujpt3oybegxplm2wqphdgchq
*logic*. 1. Intuitionistic N-system.*Normal*deductions. 2. Typed polymorphic lambda calculus. 3. Girard's*strong**normalization**proof*. 4-5. ...*Normalization**for*the N-system with the omega rule. 4. Schuette's*proof*that TI*for*ordinal notations below epsilon 0 is underivable*in*PA. 5. ...##
###
Some remarks on lengths of propositional proofs

1995
*
Archive for Mathematical Logic
*

Some open problems

doi:10.1007/s001530050030
fatcat:zs3xnde2g5evdgxmb7kjgs5q4u
*in**propositional**proof*length and*in**logical*flow*graphs*are discussed. ... We survey the best known lower bounds*on*symbols and lines*in*Frege and extended Frege*proofs*. ... Cycles*in*the*Logical*Flow*Graph*The*logical*flow*graph*of a*proof*P is a directed*graph**on*occurences of subformulas*in*P indicating the 'implicational flow' of the formulas*in*the*proof*. ...##
###
Some remarks on lengths of propositional proofs

1995
*
Archive for Mathematical Logic
*

Some open problems

doi:10.1007/bf02391554
fatcat:mo2k5kyitngj5lzehnjlv66ibu
*in**propositional**proof*length and*in**logical*flow*graphs*are discussed. ... We survey the best known lower bounds*on*symbols and lines*in*Frege and extended Frege*proofs*. ... Cycles*in*the*Logical*Flow*Graph*The*logical*flow*graph*of a*proof*P is a directed*graph**on*occurences of subformulas*in*P indicating the 'implicational flow' of the formulas*in*the*proof*. ...##
###
Identity of Proofs Based on Normalization and Generality

2003
*
Bulletin of Symbolic Logic
*

This proposal seems more promising than the other

doi:10.2178/bsl/1067620091
fatcat:2k56fbyssveqvfdafld4w2oovm
*one**for*the general*proof*theory of classical*logic*. ... Prawitz proposed to analyze identity of*proofs**in*terms of the equivalence relation based*on*reduction to*normal*formin natural deduction. ... A plenary address at the*Logic*Colloquium 2002*in*Miinster was based*on*the present paper. I am grateful to the organizers*for*inviting me to deliver this talk. ...##
###
Identity of Proofs Based on Normalization and Generality
[article]

2004
*
arXiv
*
pre-print

The first approach, which stems from Prawitz, Kreisel and Lambek, and is based

arXiv:math/0208094v12
fatcat:mttiom5k25bjdiad4ld4bu6d54
*on**normalization*of*proofs*, gives good results*in*intuitionistic, but not*in*classical*logic*. ...*In*general*proof*theory there are two approaches to the question of identity criteria*for**proofs*. ... A plenary address at the*Logic*Colloquium 2002*in*Münster was based*on*the present paper. I am grateful to the organizers*for*inviting me to deliver this talk. ...##
###
Page 7604 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

Unfortunately, as they admit

*in*the corrigendum, there are prob- lems with their*proof*, but they claim it still provides a*strong**normalization**proof**for*Au-calculus. G. E. ... This is an interesting and very well written paper*on*the com- plexity of*proofs*of*propositional*formulas. ...##
###
A Strongly Normalising Curry-Howard Correspondence for IZF Set Theory
[chapter]

2003
*
Lecture Notes in Computer Science
*

*in*IZF. ... We propose a method

*for*realising the

*proofs*of Intuitionistic Zermelo-Fraenkel set theory (IZF) by strongly normalising λ-terms. ... Notice that

*in*order to prove the

*strong*normalisation invariant

*for*system F ω.2 ++ , we first have to check the soundness of

*propositional*subtyping:

*Proposition*8 -If Σ A ≤ B, then

*for*all ρ ∈ Σ

*one*...

##
###
Priority Structures in Deontic Logic

2013
*
Theoria
*

*In*this two-level setting, we also offer novel takes

*on*vexed issues such as the Chisholm paradox and modeling

*strong*permission. ... This paper proposes a systematic application of recent developments

*in*the

*logic*of preference to a number of topics

*in*deontic

*logic*. ... The paper has also greatly benefited from invaluable discussions with Jörg Hansen

*on*the preference-based tradition

*in*deontic

*logic*, and from many helpful comments from Marek Sergot and the participants ...

##
###
A self-dual language for graph theory

1979
*
Journal of combinatorial theory. Series B (Print)
*

A sense is considered

doi:10.1016/0095-8956(79)90068-6
fatcat:ezjvaa2l65b7rprdigwgb5mdmm
*in*which the properties expressible*in*this language are precisely the self-dual properties of*graph*theory. 00958956/79/07$2.OO/O ... A symbolic language is developed around the primitive notions of edge and spanning tree, with each spanning tree being interpreted as a binary relation*on*edges. ... (This is called disjunctive*normal*form*in**logic*.) ...##
###
Some Notes on Proofs with Alpha Graphs
[chapter]

2006
*
Lecture Notes in Computer Science
*

It is well-known that Peirce's Alpha

doi:10.1007/11787181_13
fatcat:46v34wpfabhrvkegv4tusoch6a
*graphs*correspond to*propositional**logic*(PL). Nonetheless, Peirce's calculus*for*Alpha*graphs*differs to a large extent to the common calculi*for*PL. ...*on*the number of*propositional*variables*in*the formula. ... Peirce's calculus*for*Alpha*graphs*differs to a large extent to the common calculi*for**propositional**logic*(PL). ...##
###
Autoepistemic logic

1991
*
Journal of the ACM
*

Autoepistemic

doi:10.1145/116825.116836
fatcat:ngrivoxco5czdfx36etcwcjmoy
*logic*is*one*of the principa~modes of nonmonotonic reasoning. It umties several other modes of nonmonotonic reasoning and has important applications*in**logic*programming. ... Finally, connections with stable model semantics*for**logic*programs with negation is discussed.*In*particular, it is proven that the problem of existence of stable models is NP-complete. ... The*proof*of the main result of Section 5 relies heavily*on*the analysis of the*normal*form of*Proposition*3.5. ...##
###
Two Paradigms of Logical Computation in Affine Logic?
[chapter]

2003
*
Logic for Concurrency and Synchronisation
*

We prove that such a reduction has the

doi:10.1007/0-306-48088-3_3
fatcat:xg6bf74pyzgrjl4dhdapxnw7oq
*strong**normalization*and Church-Rosser properties. ... A notion of irrelevance*in*a*proof*-net is defined and the possibility of cancelling the irrelevant parts of a*proof*-net without erasing the entire net is taken as*one*of the correctness conditions; therefore ... (ii) The cut-elimination process*for**proof*-nets modulo irrelevance*for*MAL + Mix has the*strong**normalization*and Church-Rosser property.*PROOF*. ...##
###
Creating Büchi Automata for Multi-valued Model Checking
[chapter]

2017
*
Lecture Notes in Computer Science
*

This paper presents a method to create Büchi automata

doi:10.1007/978-3-319-60225-7_15
fatcat:glawsc2gljbpnidpqyc2azkieq
*for*multi-valued model checking using quasi-Boolean*logics*. It allows*for*multi-valued*propositions*as well as multi-valued transitions. ...*In*explicit state model checking of linear temporal*logic*properties, a Büchi automaton encodes a temporal property. ... Together with the steering*logic*that was considered*in*Section 4, this will allow us to investigate execution steering based*on*abstract models [11] , building*on*our previous implementation of multi-valued ...
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