An extended joint consistency theorem for a nonconstructive logic of partial terms with definite descriptions
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 69 (2):279-292 (2001)
The logic of partial terms (LPT) is a variety of negative free logic in which functions, as well as predicates, are strict. A companion paper focused on nonconstructive LPTwith definite descriptions, called LPD, and laid the foundation for tableaux systems by defining the concept of an LPDmodel system and establishing Hintikka's Lemma, from which the strong completeness of the corresponding tableaux system readily follows. The present paper utilizes the tableaux system in establishing an Extended Joint Consistency Theorem for LPDthat incorporates the Robinson Joint Consistency Theorem and the Craig-Lyndon Interpolation Lemma. The method of proof is similar to that originally used in establishing the Extended Joint Consistency Theorem for positive free logic. Proof of the Craig-Lyndon Interpolation Lemma for formulas possibly having free variables is readily had in LPTand its intuitionistic counterpart. The paper concludes with a brief discussion of the theory of definitions in LPD.
|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
No references found.
Citations of this work BETA
Norbert Gratzl (2010). A Sequent Calculus for a Negative Free Logic. Studia Logica 96 (3):331-348.
Similar books and articles
Dan E. Willard (2002). How to Extend the Semantic Tableaux and Cut-Free Versions of the Second Incompleteness Theorem Almost to Robinson's Arithmetic Q. Journal of Symbolic Logic 67 (1):465-496.
Dick Jongh, Marc Jumelet & Franco Montagna (1991). On the Proof of Solovay's Theorem. Studia Logica 50 (1):51 - 69.
Dan E. Willard (2006). On the Available Partial Respects in Which an Axiomatization for Real Valued Arithmetic Can Recognize its Consistency. Journal of Symbolic Logic 71 (4):1189-1199.
Walter A. Carnielli (1987). Systematization of Finite Many-Valued Logics Through the Method of Tableaux. Journal of Symbolic Logic 52 (2):473-493.
Daniel Gâinâ & Andrei Popescu (2007). An Institution-Independent Proof of the Robinson Consistency Theorem. Studia Logica 85 (1):41 - 73.
Daniel Găină & Andrei Popescu (2007). An Institution-Independent Proof of the Robinson Consistency Theorem. Studia Logica 85 (1):41-73.
Hiroakira Ono (1986). Craig's Interpolation Theorem for the Intuitionistic Logic and its Extensions—a Semantical Approach. Studia Logica 45 (1):19 - 33.
Raymond D. Gumb (1984). An Extended Joint Consistency Theorem for a Family of Free Modal Logics with Equality. Journal of Symbolic Logic 49 (1):174-183.
Raymond D. Gumb (1979). An Extended Joint Consistency Theorem for Free Logic with Equality. Notre Dame Journal of Formal Logic 20 (2):321-335.
Added to index2009-01-28
Total downloads2 ( #348,658 of 1,101,095 )
Recent downloads (6 months)1 ( #290,452 of 1,101,095 )
How can I increase my downloads?