David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Logica Universalis 3 (1):59-94 (2009)
The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables (viz., metavariables for finite sets of formulas), upon the basis of the conception of model introduced in (Fuzzy Sets Syst 121(3):27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules has such class of sequent models (called its semantics ) that a rule is derivable in the calculus iff it is sound with respect to each model of the semantics. We then show how semantics of admissible rules of such calculi can be found with using a method of free models. Next, our universal approach is applied to sequent calculi for many-valued logics with equality determinant . Finally, we exemplify this application by studying sequent calculi for some of such logics.
|Keywords||sequent calculus structural rule inference derivable rule admissible rule distributive lattice many-valued logic|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Rajeev Gore, Linda Postniece & Alwen Tiu, Cut-Elimination and Proof-Search for Bi-Intuitionistic Logic Using Nested Sequents.
Alexej P. Pynko (2010). Many-Place Sequent Calculi for Finitely-Valued Logics. Logica Universalis 4 (1):41-66.
Lloyd Humberstone (2007). Investigations Into a Left-Structural Right-Substructural Sequent Calculus. Journal of Logic, Language and Information 16 (2):141-171.
Ryo Kashima (1994). Cut-Free Sequent Calculi for Some Tense Logics. Studia Logica 53 (1):119 - 135.
A. Avron & B. Konikowska (2008). Rough Sets and 3-Valued Logics. Studia Logica 90 (1):69 - 92.
Roy Dyckhoff & Sara Negri (2000). Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic Logic. Journal of Symbolic Logic 65 (4):1499-1518.
Francesca Poggiolesi (2010). Display Calculi and Other Modal Calculi: A Comparison. Synthese 173 (3):259 - 279.
Kosta Došen (1988). Sequent-Systems and Groupoid Models. I. Studia Logica 47 (4):353 - 385.
Sara Negri (2002). Varieties of Linear Calculi. Journal of Philosophical Logic 31 (6):569-590.
René Lavendhomme & Thierry Lucas (2000). Sequent Calculi and Decision Procedures for Weak Modal Systems. Studia Logica 66 (1):121-145.
Added to index2009-05-04
Total downloads10 ( #118,353 of 1,007,943 )
Recent downloads (6 months)0
How can I increase my downloads?