Infinitary Logic Has No Expressive Efficiency Over Finitary Logic

Infinitary Domain Logic for Finitary Transition Systems

The Lindenbaum algebra generated by the Abramsky ni-tary logic is a distributive lattice dual to an SFP-domain obtained as a solution of a recursive domain equation. We extend Abramsky's result by proving that the Lindenbaum algebra generated by the innnitary logic is a completely distributive lattice dual to the same SFP-domain. As a consequence soundness and completeness of the innnitary logi...

Monadic Logic of Order over Naturals has no Finite Base

A major result concerning Temporal Logics (TL) is Kamp’s theorem [Kam68, GHR94], which states that the temporal logic over the pair of modalities X until Y and Xsince Y is expressively complete for the first order fragment of monadic logic of order over the natural numbers. We show that there is no finite set of modalities B such that the temporal logic over B and monadic logic of order have th...

Finitary Open Logic Program

Supervenience and Infinitary Logic

The discussion of supervenience is replete with the use of infinitary logical operations. For instance, one may often find a supervenient property that corresponds to an infinite collection of supervenience-base properties, and then ask about the infinite disjunction of all those base properties. This is crucial to a well-known argument of Kim (1984) that supervenience comes nearer to reduction...

Infinitary Logic and Inductive Definability over Finite Structures

The extensions of first-order logic with a least fixed point operators (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [AV91b] investigated the relation of these two logics in the absence of an ordering, using a mchine ...