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From linear proofs to direct logic with exponentials
[chapter]

1997
*
Lecture Notes in Computer Science
*

Following the idea of

doi:10.1007/3540634932_10
fatcat:fi62ng247fgghmcygtnfa6tgly
*Linear*Proofs presented in 4] we introduce the Direct Logic 14] with exponentials (DLE). The logic combines Direct Logic with the exponentials of*Linear*Logic. ... For a well-chosen subclass of formulas of this logic we provide a*matrix*-characterization which can be used as a foundation for proof-search methods based on the connection calculus. ...*Completeness*and Soundness. Let 2 (F ) s and m 2 M . For every*provable*sequent ) the*matrix*i( ) is*linear*complementary and for every*linear*complementary*matrix*m the sequent ) j(m) is*provable*. ...##
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Extending the Family of Intuitionistic Many-Valued Logics Introduced by Rousseau

1986
*
Annals of the Japan Association for Philosophy of Science
*

A

doi:10.4288/jafpos1956.7.47
fatcat:a7bobiyfpvh6rera4aytvyetzi
*matrix*is*provable*if and only if it is valid. so the proof of (1) and hence of Proposition 6 is*completed*. • 3.3. ... A*matrix*K is*provable*("¥K) iff it is the end-*matrix*of some proof-figure. A*matrix*K is cut free*provable*(_?? ...##
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From QBFs to MALL and Back via Focussing

2020
*
Journal of automated reasoning
*

Thus we have that

doi:10.1007/s10817-020-09564-x
fatcat:qth4tkmaujfjpa2vqikxhuqkpi
*non*-Π f k+1 -*provability*is computable in Σ p k+1 and so, by Dfn. 5, Π f k+1 -*provability*is computable in Π p k+1 . ... Das For*completeness*, we proceed by*induction*on the size of a FMALL proof, by essentially a rule permutation argument. ... For instance here are the cases when A is a or formula, where the derivations marked IH are obtained from the*inductive*hypothesis. ...##
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Matrix-Based Constructive Theorem Proving
[chapter]

2000
*
Applied Logic Series
*

We present a coherent account of

doi:10.1007/978-94-015-9383-0_12
fatcat:psdwy6yocnhtve5oitvdf7lsxy
*matrix*methods for constructive theorem proving and show how to extend them to*inductive*theorem proving by integrating rippling techniques into the unification process ...*Matrix*methods for intuitionistic logic also are the central inference engine for program synthesis and verification. ... of*linear*logic [14, 17] . ...
The minimally required mutual

doi:10.1145/266021.266050
dblp:conf/dac/HeCP97
fatcat:2xjvtg4ccvhnpdisl7fwpcjlli
*inductances*are extracted for a*provably*stable model. ... Furthermore, it is well known that simply discarding smallest terms to sparsify the*inductance**matrix*can render the partial*inductance**matrix*indefinite and result in an unstable circuit model. ... The*complete*partial*inductance**matrix*is positive definite. It has been shown that simply discarding mutual terms can render this*matrix*indefinite. ...##
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From QBFs to MALL and back via focussing: fragments of multiplicative additive linear logic for each level of the polynomial hierarchy
[article]

2020
*
arXiv
*
pre-print

This refines the well-known results that both MALLw and MALL are PSPACE-

arXiv:1906.03611v3
fatcat:swjxpfzzerg6pjx6ob7gj3b2ua
*complete*. ... Our main result is the obtention of fragments of MALLw (MALL with weakening)*complete*for each level of the polynomial hierarchy. ... Thus we have that*non*-Π f k+1 -*provability*is computable in Σ p k+1 and so, by Dfn. 5, Π f k+1 -*provability*is computable in Π p k+1 . ...##
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Decision problems for propositional linear logic

1992
*
Annals of Pure and Applied Logic
*

propositional

doi:10.1016/0168-0072(92)90075-b
fatcat:rgznokvv2vcj7ax6hbk3ozg6ve
*linear*logic. ... Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes PSPACE-*Complete*. ... Our most significant results are that*provability*for full propositional*linear*logic is undecidable, but that*provability*becomes PSPACE*complete*when the modal storage operator is removed. ...##
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Optimization complexity of linear logic proof games

1999
*
Theoretical Computer Science
*

*linear*logic. ... A class of

*linear*logic proof games is developed, each with a numeric score that depends on the number of preferred axioms used in a

*complete*or partial proof tree. ... Acknowledgements We would like to thank Mitsu Okada and the local organizers of the

*Linear*Logic '96 Tokyo Meeting for the splendid arrangements at the conference. ...

##
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On intuitionistic many-valued logics

1986
*
Journal of the Mathematical Society of Japan
*

A g-

doi:10.2969/jmsj/03830409
fatcat:2icqjupktjevhez2l4jgosj6g4
*matrix*is maximal unprovable if it is unprovable and any proper extension of it is*provable*. 3.61. Any*matrix*is a g-*matrix*. A*matrix*is*provable*i ff it is*provable*as a g-*matrix*. D 3.62. ... A generalized*matrix*(abbreviated by `g-*matrix*') is a finite or infinite set of signed formulas. A g-*matrix*is*provable*if it contains a*provable**matrix*. ...##
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Provable Repair of Deep Neural Networks
[article]

2021
*
arXiv
*
pre-print

using piecewise-

arXiv:2104.04413v2
fatcat:zef2xrr2zbedzdmvwrgthnto7u
*linear*activation functions. ... The key insight behind both of these algorithms is the introduction of a Decoupled DNN architecture, which allows us to reduce*provable*repair to a*linear*programming problem. ... and*non*-*linear*functions. ...##
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Proof-search in type-theoretic languages: an introduction

2000
*
Theoretical Computer Science
*

The usual

doi:10.1016/s0304-3975(99)00169-3
fatcat:gy4nmmsupfeype23pw3jzbrvwu
*completeness*theorems are stated with respect to*provability*. ... judgements of*provability*of the form S proves L : Just as satisfaction relations can be deÿned by*induction*on the structure of propositions, so judgements of*provability*can be deÿned by*induction*on ...##
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Connection methods in linear logic and proof nets construction

2000
*
Theoretical Computer Science
*

Aiming at using proof nets as a tool for automated deduction in

doi:10.1016/s0304-3975(99)00176-0
fatcat:qvmalztc2vanzc5wjc4xvcjzuu
*linear*logic, we deÿne a connection-based characterization of*provability*in Multiplicative*Linear*Logic (MLL). ... This central result is illustrated with a speciÿc algorithm that is able to construct, for a*provable*MLL sequent, a set of connections, a proof net and a sequent proof. ... Theorem 5.2 (*Completeness*). If S is a sequent*provable*in MLL then the algorithm returns a proof net of S. Proof. ...##
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Substructural Verification and Computational Feasibility
[chapter]

2002
*
Foundations of Information Technology in the Era of Network and Mobile Computing
*

When

doi:10.1007/978-0-387-35608-2_41
dblp:conf/ifipTCS/Leivant02
fatcat:pq322qal2rdvxm7s3xmocmuz3u
*induction*is restricted to positive formulas, a generalization of I:~ formulas, exactly the primitive recursive functions are*provable*. ... We show here that*induction*over arbitrary formulas does not add new*provable*functions if we disallow in derivations the closing of multiple data-complex assumptions. ... For ~nstance,*linear*logic leads to polytime [6, 5] , second-order existential database queries are poly-time if the*matrix*is Horn [12, 8] , monotone*inductive*definitions (where each object is inserted ...##
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Page 1309 of Mathematical Reviews Vol. , Issue 96c
[page]

1996
*
Mathematical Reviews
*

One of the results which can be easily understood is that, if a [],-sentence whose

*matrix*is an equation is*provable*in Peano arithmetic, then there is a < €o- DR function which realizes it. ... Bistructures form a categorical model of Girard’s classical*linear*. logic in which the involution of*linear*logic is modelled, roughly speaking, by a reversal of the roles of input and output. ...##
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Linear objects: Logical processes with built-in inheritance

1991
*
New generation computing
*

Event spaces and their

doi:10.1007/bf03037173
fatcat:qhsukwvkdresrlwwu6s2kvvosa
*linear*... Is there a use for*linear*logic? To Appear ACM/IFIP PEPM, 1991. 92] P. Wadler.*Linear*types can change the world! IFIP TC 2 Conf. on Prog. Concepts and Methods, 1991. 93] P. Wadler. ... Theorem 2.3.4 (Cut-Elimination) If a sequent is*provable*in*linear*logic, then it is*provable*in*linear*logic without using the Cut rule. Proof. By*induction*on the degree of the assumed proof. ...
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