### Strong paraconsistency by separating composition and decomposition in classical logic

Peter Verdée UGent (2011) 6642. p.272-292
abstract
In this paper I elaborate a proof system that is able to prove all classical first order logic consequences of consistent premise sets, without proving trivial consequences of inconsistent premises (as in A, ¬A ⊢ B). Essentially this result is obtained by formally distinguishing consequences that are the result of merely decomposing the premises into their subformulas from consequences that may be the result of also composing ‘new’, more complex formulas. I require that, whenever ‘new’ formulas are derived, they are to be preceded by a special +-symbol and these +-preceded formulas are not to be decomposed. By doing this, the proofs are separated into a decomposition phase followed by a composition phase. The proofs are recursive, axiomatizable and, as they do not trivialize inconsistent premise sets, they define a very strong non-transitive paraconsistent logic, for which I also provide an adequate semantics.
author
organization
year
type
conference
publication status
published
subject
in
LOGIC, LANGUAGE, INFORMATION AND COMPUTATION
editor
R Goebel
volume
6642
issue title
Lecture Notes in Computer Science
pages
272 - 292
publisher
Springer
place of publication
Berlin, Germany
conference name
Logic, Language, Information and Computation : 18th International Workshop (WoLLIC - 2011)
conference location
conference start
2011-05-18
conference end
2011-05-20
ISSN
0302-9743
ISBN
364220919X
DOI
10.1007/978-3-642-20920-8_26
language
English
UGent publication?
yes
classification
C1
I have transferred the copyright for this publication to the publisher
VABB id
c:vabb:320776
VABB type
VABB-5
id
1859548
handle
http://hdl.handle.net/1854/LU-1859548
date created
2011-07-14 16:15:26
date last changed
2015-06-17 09:49:12
```@inproceedings{1859548,
abstract     = {In this paper I elaborate a proof system that is able to prove all classical first order logic consequences of consistent premise sets, without proving trivial consequences of inconsistent premises (as in A, {\textlnot}A\,\unmatched{22a2}\,B). Essentially this result is obtained by formally distinguishing consequences that are the result of merely decomposing the premises into their subformulas from consequences that may be the result of also composing {\textquoteleft}new{\textquoteright}, more complex formulas. I require that, whenever {\textquoteleft}new{\textquoteright} formulas are derived, they are to be preceded by a special +-symbol and these +-preceded formulas are not to be decomposed. By doing this, the proofs are separated into a decomposition phase followed by a composition phase. The proofs are recursive, axiomatizable and, as they do not trivialize inconsistent premise sets, they define a very strong non-transitive paraconsistent logic, for which I also provide an adequate semantics.},
author       = {Verd{\'e}e, Peter},
booktitle    = {LOGIC, LANGUAGE, INFORMATION AND COMPUTATION},
editor       = {Goebel, R},
isbn         = {364220919X},
issn         = {0302-9743},
language     = {eng},
pages        = {272--292},
publisher    = {Springer},
title        = {Strong paraconsistency by separating composition and decomposition in classical logic},
url          = {http://dx.doi.org/10.1007/978-3-642-20920-8\_26},
volume       = {6642},
year         = {2011},
}

```
Chicago
Verdée, Peter. 2011. “Strong Paraconsistency by Separating Composition and Decomposition in Classical Logic.” In Logic, Language, Information and Computation, ed. R Goebel, 6642:272–292. Berlin, Germany: Springer.
APA
Verdée, Peter. (2011). Strong paraconsistency by separating composition and decomposition in classical logic. In R. Goebel (Ed.), LOGIC, LANGUAGE, INFORMATION AND COMPUTATION (Vol. 6642, pp. 272–292). Presented at the Logic, Language, Information and Computation : 18th International Workshop (WoLLIC - 2011), Berlin, Germany: Springer.
Vancouver
1.
Verdée P. Strong paraconsistency by separating composition and decomposition in classical logic. In: Goebel R, editor. LOGIC, LANGUAGE, INFORMATION AND COMPUTATION. Berlin, Germany: Springer; 2011. p. 272–92.
MLA
Verdée, Peter. “Strong Paraconsistency by Separating Composition and Decomposition in Classical Logic.” Logic, Language, Information and Computation. Ed. R Goebel. Vol. 6642. Berlin, Germany: Springer, 2011. 272–292. Print.