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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

A.S. Troelstra
1995 Annals of Pure and Applied Logic
I 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

Mark Hepple
1997 Proceedings of the 35th annual meeting on Association for Computational Linguistics -
whereby some method 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

David Albrecht, John N. Crossley, John S. Jeavons
1997 Theoretical Computer Science
In this paper we (1) provide 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

GLYN MORRILL
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]

Ruy J.G.B. de Queiroz, Anjolina G. de Oliveira
2013 arXiv   pre-print
Indeed, in 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]

Herman Geuvers, Rob Nederpelt
2004 Lecture Notes in Computer Science
Flag style 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

Moritz Hardt, Gert Smolka
2007 Electronical Notes in Theoretical Computer Science
We present modal logic on 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]

Ruy J. G. B. De Queiroz, Dov M. Gabbay
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]

Marco Bozzano, Roberto Bruttomesso, Alessandro Cimatti, Tommi Junttila, Peter van Rossum, Stephan Schulz, Roberto Sebastiani
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]

Kai Brünnler, Richard McKinley
2008 Lecture Notes in Computer Science
Starting from 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]

Venkatesh Choppella, Christopher T. Haynes
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

Venkatesh Choppella, Christopher T. Haynes
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]

Paolo Pistone
2021 arXiv   pre-print
In this paper we argue 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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