In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...) in the paper “More modal semantics without possible worlds”, where an alternative solution was proposed. (shrink)

1. A. Heyting (1930) introduced an intermediate logic whose semantics is based on a pair of states (‘here’ and ‘there’). This logic was axiomatized by Hosoi (1966), using the sequence of intermedia...

Internationally recognized logicians present current thinking on the understanding of the role of deduction in human reasoning.

1. Reasoning about action and change, or more generally reasoning about dynamic systems, is not only central to knowledge representation and reasoning but at the heart of computer science (Fisher e...

ABSTRACT We consider the question of the complete axiomatization of a relative modal logic with composition and intersection.