Existential second-order logic and modal logic with quantified accessibility relations

Existential second-order logic and modal logic with quantified accessibility relations

This article investigates the role of arity of second-order quantifiers in existential second-order logic, also known as Σ1. We identify fragments L of Σ1 where second-order quantification of relations of arity k > 1 is (nontrivially) vacuous in the sense that each formula of L can be translated to a formula of (a fragment of) monadic Σ1. Let polyadic Boolean modal logic with identity (PBML) be...

Existential Second-order Logic over Strings Existential Second-order Logic over Strings – Modified March 1998 –

Existential second-order logic (ESO) and monadic second-order logic (MSO) have attracted much interest in logic and computer science. ESO is a much more expressive logic over word structures than MSO. However, little was known about the relationship between MSO and syntactic fragments of ESO. We shed light on this issue by completely characterizing this relationship for the prefix classes of ES...

An existential fragment of second order logic

On Quantified Modal Logic

Propositional modal logic is a standard tool in many disciplines, but first-order modal logic is not. There are several reasons for this, including multiplicity of versions and inadequate syntax. In this paper we sketch a syntax and semantics for a natural, well-behaved version of first-order modal logic, and show it copes easily with several familiar difficulties. And we provide tableau proof ...

Expressivity of Second Order Propositional Modal Logic

We consider second order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem-Rosen theorem and the GoldblattThomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of S...