David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 53 (3):397 - 416 (1994)
In this note, we will study four implicational logicsB, BI, BB and BBI. In , Martin and Meyer proved that a formula is provable inBB if and only if is provable inBBI and is not of the form of » . Though it gave a positive solution to theP - W problem, their method was semantical and not easy to grasp. We shall give a syntactical proof of the syntactical relation betweenBB andBBI logics. It also includes a syntactical proof of Powers and Dwyer's theorem that is proved semantically in . Moreover, we shall establish the same relation betweenB andBI logics asBB andBBI logics. This relation seems to say thatB logic is meaningful, and so we think thatB logic is the weakest among meaningful logics. Therefore, by Theorem 1.1, our Gentzentype system forBI logic may be regarded as the most basic among all meaningful logics. It should be mentioned here that the first syntactical proof ofP - W problem is given by Misao Nagayama .
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Hiroakira Ono & Yuichi Komori (1985). Logics Without the Contraction Rule. Journal of Symbolic Logic 50 (1):169-201.
M. E. Szabo (1971). The Collected Papers of Gerhard Gentzen. Journal of Philosophy 68 (8):238-265.
E. P. Martin & R. K. Meyer (1982). Solution to the P-W Problem. Journal of Symbolic Logic 47 (4):869-887.
Yuichi Komori (1986). Predicate Logics Without the Structure Rules. Studia Logica 45 (4):393 - 404.
Citations of this work BETA
No citations found.
Similar books and articles
Diderik Batens (2007). A Universal Logic Approach to Adaptive Logics. Logica Universalis 1 (1):221-242.
A. Avron (2000). Implicational F-Structures and Implicational Relevance Logics. Journal of Symbolic Logic 65 (2):788-802.
Sachio Hirokawa, Yuichi Komori & Misao Nagayama (2000). A Lambda Proof of the P-W Theorem. Journal of Symbolic Logic 65 (4):1841-1849.
Marek Tokarz (1979). Deduction Theorems for RM and its Extensions. Studia Logica 38 (2):105 - 111.
Hiroakira Ono (1986). Craig's Interpolation Theorem for the Intuitionistic Logic and its Extensions—a Semantical Approach. Studia Logica 45 (1):19 - 33.
Takahito Aoto (1999). Uniqueness of Normal Proofs in Implicational Intuitionistic Logic. Journal of Logic, Language and Information 8 (2):217-242.
Nobu-Yuki Suzuki (1990). Some Syntactical Properties of Intermediate Predicate Logics. Notre Dame Journal of Formal Logic 31 (4):548-559.
Ewa Orlowska (1992). Relational Proof System for Relevant Logics. Journal of Symbolic Logic 57 (4):1425-1440.
Adam Gajda, Michał Krynicki & Lesław Szczerba (1987). A Note on Syntactical and Semantical Functions. Studia Logica 46 (2):177 - 185.
Paolo Gentilini (1993). Syntactical Results on the Arithmetical Completeness of Modal Logic. Studia Logica 52 (4):549 - 564.
Added to index2009-01-28
Total downloads8 ( #368,084 of 1,789,926 )
Recent downloads (6 months)1 ( #423,018 of 1,789,926 )
How can I increase my downloads?