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Page 6804 of Mathematical Reviews Vol. , Issue 2000j
[page]

2000
*
Mathematical Reviews
*

(BR-FPN-I; Recife)

*A**normalization**procedure**for**the**equational**fragment**of**labelled**natural**deduction*. (English summary) Log. J. IGPL 7 (1999), no. 2, 173-215. ...*The*paper is written in*a*discursive style and contains various observations on*the*proper treatment*of*equality in*the*context*of**labeled**natural**deduction*. ...##
###
Natural deduction for intuitionistic linear logic

1995
*
Annals of Pure and Applied Logic
*

I

doi:10.1016/0168-0072(93)e0078-3
fatcat:qjduwk4rsffdjpsey6sjwc4ome
*for**the*exponential; in ILL+, instead*of**a*contraction rule, multiple occurrences*of**labels**for*assumptions are permitted under certain conditions; moreover, there is*a*different introduction rule*for*... I+, which is closer in spirit to*the*necessitation rule*for**the*normalizable version*of*S4 discussed by Prawitz in his monograph "*Natural**Deduction*". ... Schellinx*for*discussions and critical comments on*a*first draft*of*this paper, as well as to*the*referee*for*some useful comments. ...##
###
Maximal incrementality in linear categorial deduction

1997
*
Proceedings of the 35th annual meeting on Association for Computational Linguistics -
*

whereby some method

doi:10.3115/976909.979661
dblp:conf/acl/Hepple97
fatcat:r4qmhpfbdnd2razl4h4ndd7ugq
*of*linear logic theorem proving is used in combination with*a*system*of**labelling*that ensures only*deductions*appropriate to*the*relevant grammatical logic are allowed. ... Recent work has seen*the*emergence*of**a*common framework*for*parsing categorial grammar (CG) formalisms that fall within*the*'type-logical' tradition (such as*the*Lambek calculus and related systems), ...*For**the*implicational*fragment*,*the*set*of*formulae ~ are defined by 5 r ::=*A*[ ~'o-~-(with*A**a*nonempty set*of*atomic types). ...##
###
New Curry-Howard terms for full linear logic

1997
*
Theoretical Computer Science
*

In this paper we (1) provide

doi:10.1016/s0304-3975(97)00044-3
fatcat:ybizgr6trbbovpapzpqynwvypa
*a**natural**deduction*system*for*full first-order linear logic, (2) introduce Curry-Howard-style terms*for*this version*of*linear logic, (3) prove strong*normalization**for**the*... system, and (4). prove that given*a*proof*of*V~'x3y*a*(.~, y) and any individual term t we can compute*a*term u such that*a*(t,u) is provable. ...*The*computational*procedures**for*these proof expansions are inherently parallel in*nature*and provide*a*clear dichotomy between lazy and eager evaluation*procedures*. ...##
###
Clausal Proofs and Discontinuity

1995
*
Logic Journal of the IGPL
*

*A*suitable uni cation strategy is obtained

*for*calculi

*of*discontinuity by normalisation

*of*

*the*ground goal term followed by recursive descent and redex pattern matching on

*the*head term. ...

*The*prosodic (sublinear) aspects are encoded in

*labels*, in e ect

*the*term-structure

*of*quanti ed linear logic. ... Acknowledgements I thank Michael Moortgat and Dick Oehrle

*for*comments on this work. ...

##
###
Propositional equality, identity types, and direct computational paths
[article]

2013
*
arXiv
*
pre-print

Indeed, in

arXiv:1107.1901v3
fatcat:3i5nabnweza7rkiuoxv2v5oxlq
*a*(1994--5) proposal*for**the*formalisation*of*proofs*of*propositional equality in*the*Curry--Howard style, we have already uncovered such*a*peculiarity. ... In proof theory*the*notion*of*canonical proof is rather basic, and it is usually taken*for*granted that*a*canonical proof*of**a*sentence must be unique up to certain minor syntactical details (such as, ... Applying this same technique to*the*LND*equational**fragment*, we obtain*the**normalization*theorems*for**the**equational*logic*of**the**Labelled**Natural**Deduction*System [27, 29, 30] . ...##
###
Rewriting for Fitch Style Natural Deductions
[chapter]

2004
*
Lecture Notes in Computer Science
*

Flag style

doi:10.1007/978-3-540-25979-4_10
fatcat:dspgpihdbzf2vef3hfd2y4agpq
*Natural**Deduction*We consider*the*implicational*fragment*, so*the*set*of*formulas, Form, is built up from*a*set*of*parameters, Par, using*the*implication →. ... Then we define*the*notion*of*cut-elimination on Fitch*deductions*, which is only possible*for**deductions*that are completely unshared (*normal*forms*of**the*unsharing reduction). ... Acknowledgments We greatly acknowledge*the*very insightful comments and suggestions*of**the*referees on*the*first version*of*this paper. ...##
###
Page 5054 of Mathematical Reviews Vol. , Issue 88j
[page]

1988
*
Mathematical Reviews
*

To determine

*the*proper*label**for**a*node in*the**normal*form*of**a*derivation,*a*finite set*of*nodes*of**the*given derivation, upon which this*label*depends, is constructed explicitly. ...*The*author defines and investigates*a*primitive recursive opera- tor N, which*normalizes*infinitary derivations*of**a*Gentzen-style*natural**deduction*system*for*first-order arithmetic with*the*w-rule and ...##
###
Higher-Order Syntax and Saturation Algorithms for Hybrid Logic

2007
*
Electronical Notes in Theoretical Computer Science
*

We present modal logic on

doi:10.1016/j.entcs.2006.11.023
fatcat:l3er2uovyjgzxiv6bha6qahxa4
*the*basis*of**the*simply typed lambda calculus with*a*system*of**equational**deduction*. ... We develop*a*tableau-like semi-decision*procedure*and subsequently*a*decision*procedure**for*an alternative characterization*of*HL(@),*a*well-studied*fragment**of*Hybrid Logic. ... Acknowledgments We thank an anonymous referee*for*pointing out*a*flaw in*a*previous version*of**the*paper. We appreciate*the*time*the*editors gave us*for*reorganizing*the*results. ...##
###
Labelled Natural Deduction
[chapter]

1999
*
Trends in Logic
*

*The*Functional Interpretation

*of*Logical

*Deduction*

*for*disjunction, and ...

*The*rôle

*of*

*the*

*labels*Unlike axiomatic systems,

*natural*

*deduction*proofs need not start from axioms. ... Whereas

*the*variables

*for*individuals are handled '

*naturally*' in

*the*interpretation

*of*first-order logic with our

*labelled*

*natural*

*deduction*,

*the*introduction

*of*variables to denote contexts, or possible-worlds ...

##
###
The MathSAT 3 System
[chapter]

2005
*
Lecture Notes in Computer Science
*

*The*

*Equational*Satisfiability

*Procedure*

*The*first layer

*of*T -SOLVER is provided by

*the*

*equational*solver,

*a*satisfiability checker

*for*EUF with minor extensions

*for*arithmetic predicates and constants ... T -SOLVER consists mainly on two main layers: an

*Equational*Satisfiability

*Procedure*

*for*EUF and

*a*Linear Arithmetic

*Procedure*

*for*SEP , LA(R) and LA(Z). ...

##
###
An Algorithmic Interpretation of a Deep Inference System
[chapter]

2008
*
Lecture Notes in Computer Science
*

Starting from

doi:10.1007/978-3-540-89439-1_34
fatcat:s2onuy4y3fh35avd64ngy3y67q
*natural**deduction**for**the*conjunction-implication*fragment**of*intuitionistic logic we design*a*corresponding deep inference system together with reduction rules on proofs that allow*a*fine-grained ... We set out to find something that corresponds to deep inference in*the*same way that*the*lambda-calculus corresponds to*natural**deduction*. ... System Beta never leaves*the*strictly positive*fragment*. Full*naturality**for*i and e would allow us to leave that*fragment*. This gives us*a*lot*of*freedom. ...##
###
Source-Tracking Unification
[chapter]

2003
*
Lecture Notes in Computer Science
*

*The*semantics

*of*

*deductions*are paths over

*a*unification graph whose

*labels*form

*the*suffix language

*of*

*a*semi-Dyck set. ... (n 3 )

*for*

*a*fixed signature, where n is

*the*number

*of*vertices

*of*

*the*unification graph. ... Acknowledgment Critical feedback from

*the*anonymous referees also helped considerably in improving

*the*paper. ...

##
###
Source-tracking unification

2005
*
Information and Computation
*

*The*semantics

*of*

*deductions*are paths over

*a*unification graph whose

*labels*form

*the*suffix language

*of*

*a*semi-Dyck set. ... (n 3 )

*for*

*a*fixed signature, where n is

*the*number

*of*vertices

*of*

*the*unification graph. ... Acknowledgment Critical feedback from

*the*anonymous referees also helped considerably in improving

*the*paper. ...

##
###
A New Conjecture About Identity of Proofs
[article]

2021
*
arXiv
*
pre-print

In this paper we argue

arXiv:2110.02630v1
fatcat:7uee5kbmxrcylbkzzue3szhz6u
*for**a*new criterion*for*identity*of*proofs which arises from*the*interpretation*of*formal rules and derivations as*natural*transformations*of**a*suitable kind. ...*A*central problem in proof-theory is that*of*finding criteria*for*identity*of*proofs, that is,*for*when two distinct formal derivations can be taken as denoting*the*same logical argument. ...*A*typical example is provided by*the*conversion rules defining cut-elimination*procedures*in sequent calculus or*normalization*in*natural**deduction*. ...
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