Notre Dame Journal of Formal Logic

Decidability of Fluted Logic with Identity

William C. Purdy


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.

Article information

Notre Dame J. Formal Logic, Volume 37, Number 1 (1996), 84-104.

First available in Project Euclid: 16 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B25: Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]
Secondary: 03B20: Subsystems of classical logic (including intuitionistic logic)


Purdy, William C. Decidability of Fluted Logic with Identity. Notre Dame J. Formal Logic 37 (1996), no. 1, 84--104. doi:10.1305/ndjfl/1040067318.

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