A fine-structure analysis of first-order logic. (English) Zbl 0879.03004
Marx, Maarten (ed.) et al., Arrow logic and multi-modal logic. Stanford, CA: CSLI Publications. Studies in Logic, Language and Information. 221-247 (1996).
The present work is part of an interesting joint project with H. Andreka and J. van Benthem in which the authors decompose FOL (=First-Order Logic) into a hierarchy of well-behaving but weaker logics. In order to have a grasp on the fine structure of FOL, the authors reconstruct FOL as a propositional modal logic treating all extra-Boolean features of FOL as distinct modalities.
This paper is well written and organised as follows: 1 Introduction, 2 First-Order Logic with Generalized Semantics, 3 Polyadic Cylindric-Relativized Set Algebras and Connections with Generalised Semantics, 4 Decidability of the Universal Theory of Polyadic Cylindric-Relativized Set Algebras.
For the entire collection see [Zbl 0859.00018].
This paper is well written and organised as follows: 1 Introduction, 2 First-Order Logic with Generalized Semantics, 3 Polyadic Cylindric-Relativized Set Algebras and Connections with Generalised Semantics, 4 Decidability of the Universal Theory of Polyadic Cylindric-Relativized Set Algebras.
For the entire collection see [Zbl 0859.00018].
Reviewer: L.Esakia (Tbilisi)
MSC:
| 03B10 | Classical first-order logic |
| 03G15 | Cylindric and polyadic algebras; relation algebras |
| 03B45 | Modal logic (including the logic of norms) |
