A. Avron, Multiplicative Conjunction as an Extensional Conjunction, Logic Journal of the IGPL, 5 (1997), 181-208. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Implicational F-Structures and Implicational Relevance Logics - Avron Self-citation (Avron) (Correct)
....structures in which there is exactly one nondesignated element. Such structures will be called below (implicational) F structures, and the corresponding logics are called F logics . Algebraic structures, in which the set of nondesignated elements is a singleton, have already been introduced in [Av97] and [Av9 ] They were shown there to be very useful in investigating and understanding substructural logics. More specifically: we have demonstrated that while weakening corresponds to the assumption that there is exactly one designated truth value, contraction has strong connections with the ....
....was shown already in [Av84] We still do not have, however, strong completeness, since again (A B) A j= A A but A (B A) 6 RMI A. ffl We have the following strengthening of theorems III.1.2 and IV.2: IV.7 Theorem. T j= A A iff there exists B such that T RMI (A B) A. Proof: In [Av97] it is proved that in the full multiplicative language, T j= A A iff there exists B such that T RMIm A Omega B. Here B can be assumed to be a purely implicational formula (since if p 1 ; p k are the atomic variables in B then B ( p 1 p 2 Delta Delta Delta p k ) p 1 p 2 ....
[Article contains additional citation context not shown here]
Avron A., Multiplicative Conjunction as an Extensional Conjunction, Logic Journal of the IGPL, vol. 5 (1997), pp. 181-208.
Two Types of Multiple-Conclusion Systems - Avron (1998) (2 citations) Self-citation (Avron) (Correct)
....are equivalent, and both admit cut elimination. The next system is the natural m sequential extension of RM0im . 3 We could have easily included as well, but this is definable as . In linear logic and (or 0 and as in [15] but unlike [19] are considered to be additives . In [8] we explain why it is safe (and even preferable) to take them as a part of the multiplicative fragment. 702 Two Types of Multiple Conclusion Systems (2) The m sequential system RMIim . Axioms: A ) A Gamma; Delta ( Delta 6= Logical Rules: The m sequential versions of the logical ....
....mingle rules by the (hypersequential) mix rule. Note As noted above, RM0im , RMIim , and RMim are either natural conservative extensions or else fragments of well known systems. RMI h im and RM h im are in turn the Lim fragments of the systems SRMI and SRM (respectively) of [8] (this follows either by cut elimination or can be shown by semantical methods) The system RM0 h im , on the other hand, is introduced and investigated here for the first time. Since all the six systems we have just introduced are purely multiplicative, there is no difference between the ....
[Article contains additional citation context not shown here]
Avron A., Multiplicative Conjunction as an Extensional Conjunction, Logic Journal of the IGPL, vol. 5 (1997), pp. 181-208.
Multiplicative Conjunction and an Algebraic Meaning of Contraction .. - Avron Self-citation (Avron) (Correct)
.... mix rule: from Gamma 1 ) Delta 1 and Gamma 2 ) Delta 2 infer Gamma 1 ; Gamma 2 ) Delta 1 ; Delta 2 . This fact entails both propositions in the case of RMI b m . 8 Note. In [Gi87] the constant belongs to the additives , not to the official multiplicative fragment of Linear Logic. In [Av97] we argue in some length why considering it as a multiplicative constant is more reasonable. 9 In what follows we shall encounter some other indications that it is very natural to include (and ) in the multiplicative fragment. This inclusion will prove to be very useful in what follows. 3 ....
.... B) C Rm C Omega ( B B Omega B) Proof of the Lemma: It is not difficult to check that the corresponding sequent is provable in GRm . Alternatively, one can reason as follows: Let be B B Omega B. Then both 10 A shorter proof, using a semantic argument, can be found in [Av97]. and B are theorems of Rm . From the assumption (A B) C it follows in Rm that C A Omega B. Thus, the assumption A C and the validity of B together imply C C Omega . But C C Omega is a theorem of Rm , because is. This and C C Omega yield ....
[Article contains additional citation context not shown here]
Avron A., Multiplicative Conjunction as an Extensional Conjunction, LOgic Journal of the IGPL, vol. 5 (1997), pp. 181-208.
Combining Paraconsistency and Relevance - Avron (Correct)
No context found.
A. Avron, Multiplicative Conjunction as an Extensional Conjunction, Logic Journal of the IGPL, 5 (1997), 181-208.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC