Logically defined subsets of Nk

Algebraic characterization of logically defined tree languages

We give an algebraic characterization of the tree languages that are defined by logical formulas using certain Lindström quantifiers. An important instance of our result concerns first-order definable tree languages. Our characterization relies on the usage of preclones, an algebraic structure introduced by the authors in a previous paper, and of the block product operation on preclones. Our re...

The Minimal Logically-Defined NP-Complete Problem

On Logically Defined Recognizable Tree Languages

We provide an algebraic characterization of the expressive power of various naturally defined logics on finite trees. These logics are described in terms of Lindström quantifiers, and particular cases include first-order logic and modular logic. The algebraic characterization we give is expressed in terms of a new algebraic structure, finitary preclones, and uses a generalization of the block p...

Typicality in logically defined categories: exemplar-similarity versus rule instantiation.

A rule-instantiation model and a similarity-to-exemplars model were contrasted in terms of their predictions of typicality judgments and speeded classifications for members of logically defined categories. In Experiment 1, subjects learned a unidimensional rule based on the size of objects. It was assumed that items that maximally instantiated the rule were those farthest from the category boun...

Generalised Integer Programming Based on Logically Defined Relations

Many combinatorial optimisation problems can be modelled as integer linear programs. We consider a class of generalised integer programs where the constraints are allowed to be taken from a broader set of relations (instead of just being linear inequalities). The set of allowed relations is defined using a many-valued logic and the resulting class of relations have provably strong modelling pro...