Graduate studies at Western
Notre Dame Journal of Formal Logic 37 (1):84-104 (1996)
|Abstract||Fluted logic is the restriction of pure predicate logic to formulas in which variables play no essential role. Although fluted logic is significantly weaker than pure predicate logic, it is of interest because it seems closely to parallel natural logic, the logic that is conducted in natural language. It has been known since 1969 that if conjunction in fluted formulas is restricted to subformulas of equal arity, satisfiability is decidable. However, the decidability of sublogics lying between this restricted (homogeneous) fluted logic and full predicate logic remained unknown. In 1994 it was shown that the satisfiability of fluted formulas without restriction is decidable, thus reducing the unknown region significantly. This paper further reduces the unknown region. It shows that fluted logic with the logical identity is decidable. Since the reflection functor can be defined in fluted logic with identity, it follows that fluted logic with the reflection functor also lies within the region of decidability. Relevance to natural logic is increased since the identity permits definition of singular predicates, which can represent anaphoric pronouns|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
William C. Purdy (2002). Complexity and Nicety of Fluted Logic. Studia Logica 71 (2):177 - 198.
William C. Purdy (1996). Fluted Formulas and the Limits of Decidability. Journal of Symbolic Logic 61 (2):608-620.
Witold Marciszewski (ed.) (2006). Issues of Decidability and Tractability. University of Białystok.
Mojżesz Presburger & Dale Jabcquette (1991). On the Completeness of a Certain System of Arithmetic of Whole Numbers in Which Addition Occurs as the Only Operation. History and Philosophy of Logic 12 (2):225-233.
Joanna Golinska-Pilarek (2012). On Decidability of a Logic for Order of Magnitude Qualitative Reasoning with Bidirectional Negligibility. In Luis Farinas del Cerro, Andreas Herzig & Jerome Mengin (eds.), Logics in Artificial Intelligence. Springer.
Mark Reynolds (1994). Axiomatisation and Decidability Off Andp in Cyclical Time. Journal of Philosophical Logic 23 (2):197 - 224.
Merlijn Sevenster (2010). Decidability of Independence-Friendly Modal Logic. Review of Symbolic Logic 3 (3):415-441.
Aris Noah (1980). Predicate-Functors and the Limits of Decidability in Logic. Notre Dame Journal of Formal Logic 21 (4):701-707.
Emanuel Kieroński & Martin Otto (2012). Small Substructures and Decidability Issues for First-Order Logic with Two Variables. Journal of Symbolic Logic 77 (3):729-765.
Frank Wolter (1997). Completeness and Decidability of Tense Logics Closely Related to Logics Above K. Journal of Symbolic Logic 62 (1):131-158.
E. William Chapin (1971). The Strong Decidability of Cut Logics. II. Generalizations. Notre Dame Journal of Formal Logic 12 (4):429-434.
Philip Kremer (1999). Relevant Identity. Journal of Philosophical Logic 28 (2):199-222.
J. Almog (1980). Semantical Considerations on Modal Counterfactual Logic with Corollaries on Decidability, Completeness, and Consistency Questions. Notre Dame Journal of Formal Logic 21 (2):467-479.
Added to index2010-08-24
Total downloads2 ( #248,212 of 757,557 )
Recent downloads (6 months)0
How can I increase my downloads?