Studia Logica

Two different kinds of multiple-conclusion consequence relations taken from Shoesmith and Smiley (Multiple-conclusion logic, Cambridge University Press, Cambridge, 1978) and Galatos and Tsinakis (J Symb Logic 74:780–810, 2009) or Nowak (Bull Sect ...

We begin with the idea that lines of reasoning are continuous mental processes and develop a notion of continuity in proof. This requires abstracting the notion of a proof as a set of sentences ordered by provability. We can then distinguish ...

Hahn’s embedding theorem asserts that linearly ordered abelian groups embed in some lexicographic product of real groups. Hahn’s theorem is generalized to a class of residuated semigroups in this paper, namely, to odd involutive commutative ...

In this paper, a particular extension of the constitutive bi-modal logic for single-agent subset spaces will be provided. That system, which originally was designed for revealing the intrinsic relationship between knowledge and topology, has been ...

In Hannes Leitgeb’s article What truth depends on (Leitgeb in J Philos Logic 34:155–192, 2005) the author provides a formally correct and materially adequate truth definition for the set of all grounded sentences, defined as the least fixed point ...

A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have a ...

We develop a general theory of FDE-based modal logics. Our framework takes into account the four-valued nature of FDE by considering four partially defined modal operators corresponding to conditions for verifying and falsifying modal necessity ...

I build a canonical model for constant domain basic first-order logic (${\mathsf{BQL}}_{\mathsf{CD}}$), the constant domain first-order extension of Visser’s basic propositional logic, and use the canonical model to verify that ${\mathsf{BQL}}_{\mathsf{CD}}$ satisfies the disjunction and ...