It is known that the implicational fragment of the relevant logic E is complete with respect to the class of Urquhart's models, where a model consists of a semilattice and a set of possible worlds. This paper shows that some implicational relevant logics, which are obtained from E by adding axioms, are complete with respect to the class of Urquhart's models with certain conditions. To show this...

In this paper, I show that scales (or hierarchies) have been appealed to in various functions: They have been used to formulate descriptive generalizations (on a single language), and to formulate cross-linguistic generalizations. They have also been used for binary relations, and for implicational relations among more than two items on the scale. This yields four uses of scales (descriptive re...

Much useful new information (e.g. information in news reports) is often that which is surprising or unexpected. In other words, we harbour many expectations about the world, and when any of these expectations are violated (i.e. made inconsistent) by new information, we have a strong indicator that the information is interesting for us. An expectation can be compared with an integrity constraint...

This study investigated whether L2 phonological learning can be characterized as a gradual and systematically patterned replacement of non-native segments by native segments in learners’ speech, conforming to a two-stage implicational scale. The study adopted a dynamic approach to language variation based on Gatbonton’s (1978) gradual diffusion framework. Participants were 40 Québec Francophone...

Implicational partial Galois logics and some of their semilinear extensions, such as extensions satisfying abstract dual connection properties, have been introduced together with relational semantics. However, similar residuated, residuated properties not. This paper fills the gaps by introducing those To this end, class implicational (dual) residuated-connected prelinear gaggle is defined it v...