A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Proof Theory and Algebra in Substructural Logics
[chapter]

2011
*
Lecture Notes in Computer Science
*

Proving cut elimination

doi:10.1007/978-3-642-22119-4_3
fatcat:vcf3dmefgzc4zhm2gnwvqiitfe
*for*such*a*generalized*sequent**calculus*is closely*related*to proving that*a*variety is closed under the corresponding generalized completions. ... Finding*a*new variant of*sequent**calculus*(such as hypersequent*calculus*) amounts to finding*a*new variant of MacNeille completions (generalizations of Dedekind's completion Q → R). ... Proving cut elimination*for*such*a*generalized*sequent**calculus*is closely*related*to proving that*a*variety is closed under the corresponding generalized completions. ...##
###
Equivalential Gentzen systems and the reduced matrices of the Gentzen systems associated with finitely valued logics

2006
*
Reports on Mathematical Logic
*

Font

dblp:journals/rml/GilR06
fatcat:evz4ahm6yjenhpqloftcvtn5li
*for*his valuable comments on*a*draft of the paper. Also, we would like to thank an anonymous referee whose comments were really helpful. ... exactly the consequence*relation*determined by the*sequent**calculus*. ... Let L be*a*finite L-*algebra*.*A*VL-Gentzen system is*a*Gentzen system determined by*a*VL-*sequent**calculus*. ...##
###
The categorical equivalence between disjunctive sequent calculi and algebraic L-domains
[article]

2020
*
arXiv
*
pre-print

This paper establishes

arXiv:1904.03671v2
fatcat:6ixowcpjwjdd3hoafryuej7xha
*a*purely syntactic representation*for*the category of*algebraic*L-domains with Scott-continuous functions as morphisms. ... The central tool used here is the notion of logical states, which builds*a*bridge between disjunctive*sequent*calculi and*algebraic*L-domains. ... We only illustrate this*for*the rule (Lwk): Proposition 3 . 5 . 35*For*the disjunctive*sequent**calculus*(L(P D ), ⊢ D ) associated with*a*given*algebraic*L-domain (D, ≤), we have (1)*a*formula ϕ is*a*...##
###
Cut-free display calculi for relation algebras
[chapter]

1997
*
Lecture Notes in Computer Science
*

We extend Belnap's Display Logic to give

doi:10.1007/3-540-63172-0_40
fatcat:3ctbkynpw5cyph6sjwgqajvwvm
*a*cut-free Gentzen-style*calculus**for**relation**algebras*. ... It also appears to be the rst purely propositional Gentzen-style*calculus**for**relation**algebras*. ... Acknowledgments: Thanks to Lev Gordeev, Wolfgang Heinle, Greg Restall and Timothy Surendonk*for*many helpful discussions. ...##
###
Program Logics of Renominative Level with the Composition of Predicate Complement

2019
*
International Conference on Information and Communication Technologies in Education, Research, and Industrial Applications
*

We introduce

dblp:conf/icteri/NikitchenkoSS19
fatcat:ah4lbndnqffslc6alji7bssqdm
*a*special consequence*relation**for*this logic, construct*a**sequent**calculus*, and prove its soundness and completeness. ... One of the methods involves extension of program*algebras*with the composition of predicate complement. This permits to modify rules of the logic making them sound. ... We construct*a**sequent**calculus*C QCR*for**relation*|= IR . The main objects of this*calculus*are*sequents*. Here we consider only the case with finite*sequents*. ...##
###
From Kripke Models to Algebraic Counter-Valuations
[chapter]

1998
*
Lecture Notes in Computer Science
*

Starting with

doi:10.1007/3-540-69778-0_26
fatcat:gvkn5hsjorfwnnep5un56nmj7e
*a*derivation in the refutation*calculus*CRIP of Pinto and Dyckhoff, we give*a*constructive*algebraic*method*for*determining the values of formulas of intuitionistic propositional logic in ... The values of compound formulas are computed pointwise from the values on atoms, in contrast to the non-local determination of forcing*relations*in*a*Kripke model based on classical reasoning. ... In Pinto and Dyckhoff (1995) ,*a**related*refutation*calculus*CRIP was given,*for*showing underivability of*a**sequent*Γ ⇒ ∆. ...##
###
Lambek-Grishin Calculus: Focusing, Display and Full Polarization
[article]

2020
*
arXiv
*
pre-print

LG-

arXiv:2011.02895v1
fatcat:vw7hdkt73rc2bj5aahqnwc4ir4
*algebras*: this amounts to*a*semantic proof of the so-called completeness of focusing, given that the standard (display)*sequent**calculus**for*Lambek-Grishin logic is complete w.r.t. ... We introduce*a*novel focused display*calculus*fD.LG and*a*fully polarized*algebraic*semantics FP.LG*for*Lambek-Grishin logic by generalizing the theory of multi-type calculi and their*algebraic*semantics ... maps sending an element to its copy in the appropriate sub-*algebra*of*A*G , and finally,*for*each*A*, B in the appropriate sub-*algebra*of*A*G ,*for*each weakening*relation*R in*A*G , and*for*each binary ...##
###
Decision methods for linearly ordered Heyting algebras

2005
*
Archive for Mathematical Logic
*

The decision problem

doi:10.1007/s00153-005-0321-z
fatcat:coaw2zsen5e2fccwnte4cwrpvq
*for*positively quantified formulae in the theory of linearly ordered Heyting*algebras*is known, as*a*special case of work of Kreisel, to be solvable;*a*simple solution is here presented ... , inspired by*related*ideas in Gödel-Dummett logic. ... (*a*Fellowship*for*the first author). ...##
###
Page 3271 of Mathematical Reviews Vol. , Issue 85h
[page]

1985
*
Mathematical Reviews
*

See

*a*paper by D. J. Foulis and C. H. Randall {ibid. 14 (1984), no. 1, 65-81]*for*an opposing view. Jeffrey Bub (London, Ont.) Maddux, Roger (1-IA) 85h:03067*A**sequent**calculus**for**relation**algebras*. ...*A*. Tarski provided*a*double foundation*for*the*calculus*of rela- tions. His semantic approach led to the universal*algebraic*concept of*a**relation**algebra*. ...##
###
Page 7344 of Mathematical Reviews Vol. , Issue 2000j
[page]

2000
*
Mathematical Reviews
*

It is then shown (Theorem 3.1) that consequence

*relations*form*a*category MLS (*for*Multi-Lingual*Sequents*) whose objects (called coherent*sequent*calculi) are*algebras*L endowed with*a*consequence*relation*... The strong proximity lattice associated to*a*coherent*sequent**calculus*is ob- tained by factoring out logical equivalence and taking implication*for*the approximation*relation*. ...##
###
Multi Lingual Sequent Calculus and Coherent Spaces

1997
*
Electronical Notes in Theoretical Computer Science
*

We study

doi:10.1016/s1571-0661(05)80160-4
fatcat:3nv4xskxmzcxhanqwg5tmkezvq
*a*Gentzen style*sequent**calculus*where the formulas on the left and right of the turnstile need not necessarily come from the same logical system. ... We propose*a*di erent cut rule which addresses this problem. The new cut rule can be used as*a*basis*for*composition in*a*suitable category of logical systems. ... The previous three lemmas together entail the following result: Theorem 8.7*A*binary*relation*on nite sets from*a*term*algebra*L over generators B is*a*coherent*sequent**calculus*if and only if j B B has ...##
###
Unified correspondence and proof theory for strict implication

2016
*
Journal of Logic and Computation
*

Lambek

doi:10.1093/logcom/exw012
fatcat:b46elixh4nelfjxt6whkicpjdq
*calculus*(BDFNL). ... Gentzen-style cut-free*sequent*calculi*for*BDFNL and its extensions with analytic rules which are transformed from strict implication*sequents*, are developed. ... Alessandra Palmigiano (Delft University of Technology)*for*her comments on drafts of this paper, and the reviewers*for*their helpful comments on the submitted version. ...##
###
Sequent Calculi for Semi-De Morgan and De Morgan Algebras
[article]

2016
*
arXiv
*
pre-print

*A*contraction-free and cut-free

*sequent*

*calculus*G3SDM

*for*semi-De Morgan

*algebras*, and

*a*structural-rule-free and single-succedent

*sequent*

*calculus*G3DM

*for*De Morgan

*algebras*are developed. ... G3DM is embedded into

*a*

*sequent*

*calculus*

*for*classical propositional logic. G3SDM is embedded into the

*sequent*

*calculus*G3ip

*for*intuitionistic propositional logic. ...

*A*

*Sequent*

*Calculus*

*for*De Morgan

*Algebras*In this section, we shall present

*a*single-conclusion

*sequent*

*calculus*G3DM

*for*De Morgan

*algebras*. ...

##
###
Page 3921 of Mathematical Reviews Vol. , Issue 96g
[page]

1996
*
Mathematical Reviews
*

To provide

*a*fitting*for*the associativity of the concatenation 96¢:03107 in the*sequent**calculus*the following should hold in channel the- ory: (Su)(s-4u and ux) <=> (3v)(s4x andt4v). ... The central part of the paper gives*a**sequent**calculus*which is sound and complete with respect to this*algebra*. Moreover, it has the cut property and is also decidable. ...##
###
A Mechanised Proof System for Relation Algebra Using Display Logic
[chapter]

1998
*
Lecture Notes in Computer Science
*

Our implementation is the rst mechanisation of any display

doi:10.1007/3-540-49545-2_18
fatcat:hrlp65zylraxxfgi5yoomcuvki
*calculus*, but also provides*a*useful interactive proof assistant*for**relation**algebra*. ... We describe an implementation of the Display Logic*calculus**for**relation**algebra*as an Isabelle theory. ... The second author is supported by the Australian Research Council via*a*Queen Elizabeth II Fellowship. ...
« Previous

*Showing results 1 — 15 out of 4,182 results*