It is well known that the model categories of universal Horn theories are locally presentable, hence essentially algebraic [2]. In the special case of quasivarieties a direct translation of the implicational syntax into the essentially equational one is known [1]. Here we present a similar translation for the general case, showing at the same time that many relationally presented Horn classes a...

It is widely known that closure operators on finite sets can be represented by sets of implications (also known as inclusion dependencies) as well as by formal contexts. In this paper we survey known results and present new findings concerning time and space requirements of diverse tasks for managing closure operators, given in contextual, implicational, or black-box representation. These tasks...

We present a system of natural deduction and associated term calculus for intuitionistic non-commutative linear logic (INCLL) as a conservative extension of intuitionistic linear logic. We prove subject reduction and the existence of canonical forms in the implicational fragment. We also illustrate by means of an example how the proof term calculus can be employed in the setting of logical fram...

Properties of programs can be formulated using various techniques: dataflow analysis, abstract interpretation and type-like inference systems. This paper reconstructs strictness analysis (establishing when function parameters are evaluated in a lazy language) as a dataflow analysis by expressing the dataflow properties as an effect system. Strictness properties so expressed give a clearer opera...

Lukasiewicz implication algebras are the {→, 1}-subreducts of MV algebras. They are the algebraic counterpart of SuperLukasiewicz Implicational Logics. We give a description of free Lukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Lukasiewicz implication algebra is isomorphic to ⋃ x∈X [xθ) for a certain congruence θ over the |X|-...

Even though the most important questions about the acquisition of (L2) sound systems concern change over time (like the effect of age of onset; acquisition orders, perception vs. production; implicational relationships), most research has investigated the outcomes of phonological development rather than the process itself. I will argue that only a longitudinal, processbased approach can truly i...

We investigate properties of monadic purely negational fragment of Intuitionistic Control Logic (ICL). This logic arises from Intuitionistic Propositional Logic (IPL) by extending language of IPL by additional new constant for falsum. Having two different falsum constants enables to define two forms of negation. We analyse implicational relations between negational monadic formulae and present ...