Studia Logica

We present a formalization of collections that Cornelius Castoriadis calls “magmas”, especially the property which mainly characterizes them and distinguishes them from the usual cantorian sets. It is the property of their elements to depend on ...$$$$$$$$$$$$$$$$$$${}^{}$$\mathcal{}$$$$$${}_{}$$\mathrm{}$${}_{\mathrm{}}$${}_{\mathrm{}}{}_{}$${}_{}{}_{}{}_{}$$$$\mathrm{}$${}_{}{}_{}$${}_{}$$$${}_{\mathrm{}}{}_{}$$$${\mathrm{}}^{}$${\mathrm{}}^{}$${\mathrm{}}^{}$

In the framework of algebras with infinitary operations, the equational theory of ${\bigvee }_{\kappa }$-complete Heyting algebras or Heyting $\kappa$-frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of ...$$$\mathrm{}$

This paper deals with substructural nuclear (image-based) logics and their algebraic and Kripke-style semantics. More precisely, we first introduce a class of substructural logics with connective N satisfying nucleus property, called here ...

Let $\mathbf{K}$ and $\mathbf{M}$ be locally finite quasivarieties of finite type such that $\mathbf{K}\subset \mathbf{M}$. If $\mathbf{K}$ is profinite then the filter $[\mathbf{K},\mathbf{M}]$ in the quasivariety lattice $\text{Lq}(\mathbf{M})$ is an atomic lattice and $\mathbf{K}$ has an independent quasi-equational basis relative to $\mathbf{M}$. Applications ...

An integral subresiduated lattice ordered commutative monoid (or integral srl-monoid for short) is a pair $(\mathbf{A},Q)$ where $\mathbf{A}=(A,\wedge ,\vee ,·,1)$ is a lattice ordered commutative monoid, 1 is the greatest element of the lattice $(A,\wedge ,\vee )$ and Q is a subalgebra of ...$$$$$$$\mathrm{}$$\mathrm{}$${\mathsf{}}^{\mathsf{}}$${\mathsf{}}^{\mathsf{}}$${\mathsf{}}^{\mathsf{}}$${\mathsf{}}^{\mathsf{}}$

In one of his papers, JC Beall advanced a new and interesting interpretation of Weak Kleene logic, in terms of on-topic/off-topic. In brief, Beall suggests to read the third value as off-topic, whereas the two classical values are read as true and ...

Weak ontic necessity is the ontic necessity expressed by “should” or “ought to”. An example of it is “I should be dead by now”. A feature of this necessity is that whether it holds is irrelevant to whether its underlying proposition holds. This ...