11 papers
Axiomatization via translation: Hiz's warning for predicate logic
Guillermo Badia, John N. Crossley, Lloyd Humberstone
The problems of logical translation of axiomatizations and the choice of primitive operators have surfaced several times over the years. An early issue was raised by H. Hi{\. z} in…
Omitting Types Theorem in hybrid-dynamic first-order logic with rigid symbols
Daniel Gaina, Guillermo Badia, Tomasz Kowalski
In the the present contribution, we prove an Omitting Types Theorem (OTT) for an arbitrary fragment of hybriddynamic first-order logic with rigid symbols (i.e. symbols with fixed i…
Maximality of bi-intuitionistic propositional logic
Grigory Olkhovikov, Guillermo Badia
In the style of Lindström's theorem for classical first-order logic, this article characterizes propositional bi-intuitionistic logic as the maximal (with respect to expressive pow…
A Lindström theorem for intuitionistic first-order logic
Grigory Olkhovikov, Guillermo Badia, Reihane Zoghifard
We extend the main result of (G. Badia and G. Olkhovikov. A Lindström theorem for intuitionistic propositional logic. Notre Dame Journal of Formal Logic, 61 (1): 11--30 (2020)) to…
How Much Propositional Logic Suffices for Rosser's Essential Undecidability Theorem?
Guillermo Badia, Petr Cintula, Petr Hajek +1
In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well know…
Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic
Guillermo Badia, Vicent Costa, Pilar Dellunde +1
This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntacti…