Relevant implication and the weak deduction theorem
Studia Logica 46 (3):239 - 245 (1987)
| Abstract | It is shown that the implicational fragment of Anderson and Belnap's R, i.e. Church's weak implicational calculus, is not uniquely characterized by MP (modus ponens), US (uniform substitution), and WDT (Church's weak deduction theorem). It is also shown that no unique logic is characterized by these, but that the addition of further rules results in the implicational fragment of R. A similar result for E is mentioned | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,701 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesBeata Konikowska (1990). A Two-Valued Logic for Reasoning About Different Types of Consequence in Kleene's Three-Valued Logic. Studia Logica 49 (4):541 - 555.
Janusz Czelakowski (1986). Local Deductions Theorems. Studia Logica 45 (4):377 - 391.
Dov M. Gabbay & Nicola Olivetti (1998). Algorithmic Proof Methods and Cut Elimination for Implicational Logics Part I: Modal Implication. Studia Logica 61 (2):237-280.
Nikolaos Galatos & Hiroakira Ono (2006). Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics Over FL. Studia Logica 83 (1-3):279 - 308.
Sachio Hirokawa, Yuichi Komori & Misao Nagayama (2000). A Lambda Proof of the P-W Theorem. Journal of Symbolic Logic 65 (4):1841-1849.
Janusz Czelakowski (1985). Algebraic Aspects of Deduction Theorems. Studia Logica 44 (4):369 - 387.
Ryo Kashima & Norihiro Kamide (1999). Substructural Implicational Logics Including the Relevant Logic E. Studia Logica 63 (2):181-212.
Takahito Aoto (1999). Uniqueness of Normal Proofs in Implicational Intuitionistic Logic. Journal of Logic, Language and Information 8 (2):217-242.
Ross T. Brady (1993). Rules in Relevant Logic — II: Formula Representation. Studia Logica 52 (4):565 - 585.
M. W. Bunder (1982). Deduction Theorems for Weak Implicational Logics. Studia Logica 41 (2-3):95 - 108.
Analytics
Monthly downloads
Sorry, there are not enough data points to plot this chart.
|
Added to index2009-01-28Total downloads1 ( #274,921 of 549,125 )Recent downloads (6 months)0How can I increase my downloads? |
My notes
Discussion
