On the potential for illogic with logically defined outcomes

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...

The Minimal Logically-Defined NP-Complete Problem

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...

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...

ANCHOR: logically-centralized security for Software-Defined Networks

Software-defined networking (SDN) decouples the control and data planes of traditional networks, logically centralizing the functional properties of the network in the SDN controller. While this centralization brought advantages such as a faster pace of innovation, it also disrupted some of the natural defenses of traditional architectures against different threats. The literature on SDN has mo...