The question of the expressive power of a given logical language with Kripke relational semantics has at least two dimensions: (1) what the language can say about frames, and (2) what it can say about models. The Goldblatt-Thomason theorem provides a model-theoretic characterisation of modal axiomatisability for elementary classes of frames in terms of closure under taking generated subframes, disjoint unions, bounded morphic images, and reflection of ultrafilter extensions. Goldblatt also provides a similar characterisation for axiomatisability in intuitionistic logic of classes of models rather than frames. In this article we provide analogous results for bi-intuitionistic logic, a natural expressive extension of intuitionistic logic obtained by adding a binary connective dual to the intuitionistic implication, introduced in the 1970s independently by Dieter Klemke and Cecylia Rauszer. Together with previous results, such as a van Benthem bisimulation characterisation theorem and a Lindstrom theorem, this provides a complete picture of the expressive power of propositional bi-intuitionistic logic.
We develop a set-theoretic translation of a normal modal extension $T_m$ of a recursively axiomatizable first-order theory $T$. We first pass to the Henkin expansion of the underlying language by adding witness constants and work with the sentence algebra of this expansion. The translation is constructed using the corr...
RmbC is a self-extensional paraconsistent logic in the family of Logics of Formal Inconsistency (LFIs). This system is obtained from mbC (the basic LFI) by adding the replacement property via two global inference rules. RmbC is characterized by a non-explosive negation $\neg$ and a consistency operator $\circ$, which r...
The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzm\"uller and Scott's Notes on G\"odel's and Scott's variants of the ontological argument (2025), reaches beyond the modal object language of the arguments: its property quantifiers range over terms that may also express nomin...
In this paper, by a de re modal logic of terms, we mean a set of tautologies determined by a given semantics. We present a comprehensive study of several such semantics. First, we analyse semantics with a natural interpretation of de re modal propositions. We use the Johnson–Thomason models, but reject their four a...
A. Pietruszczak· Studia Logica: An Internatio...· 0 citations
In this paper we propose a reconstruction of the theory of multiple generality in Stoic Logic using the Natural Term Logic (NTL) developped by the author in \cite{ntl}. Contrary to a frequent misconception, it can be shown conclusively, based on the available evidence, that Stoic logic was far more than a mere proposit...
Sequent-style tableaux are a refutation calculus in which each node of the refutation tree carries a finite block of formulae and the structural rules are absorbed into the data structure and the closure criterion. In their original, classical form they rest on an involutive De Morgan negation and on closure upon a com...
Simone Cuconato· 0 citations
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