Tractability frontiers in probabilistic team semantics and existential second-order logic over the reals

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

Probabilistic Inference and Monadic Second Order Logic

This paper combines two classic results from two different fields: the result by Lauritzen and Spiegelhalter [21] that the probabilistic inference problem on probabilistic networks can be solved in linear time on networks with a moralization of bounded treewidth, and the result by Courcelle [10] that problems that can be formulated in counting monadic second order logic can be solved in linear ...

One Quantifier Will Do in Existential Monadic Second-Order Logic over Pictures

We show that every formula of the existential fragment of monadic second-order logic over picture models (i.e., nite, two-dimensional , coloured grids) is equivalent to one with only one existential monadic quantiier. The corresponding claim is true for the class of word models ((Tho82]) but not for the class of graphs ((Ott95]). The class of picture models is of particular interest because it ...

Incremental Algorithms for Local Search from Existential Second-Order Logic

Local search is a powerful and well-established method for solving hard combinatorial problems. Yet, until recently, it has provided very little user support, leading to time-consuming and error-prone implementation tasks. We introduce a scheme that, from a high-level description of a constraint in existential second-order logic with counting, automatically synthesises incremental penalty calcu...