4 citations · 12 across the 19 of their papers we have counts for
21 papers
Definable Classes of Models and Frames in Bi-intuitionistic Logic
Guillermo Badia, Tomasz Kowalski, Grigory Olkhovikov
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) w…
Asymptotic truth-value laws in many-valued logics
Guillermo Badia, Xavier Caicedo, Carles Noguera
This paper studies which truth-values are most likely to be taken on finite models by arbitrary sentences of a many-valued predicate logic. We obtain generalizations of Fagin's cla…
First-order friendliness
Guillermo Badia, David Clement Makinson
In this note we study a counterpart in predicate logic of the notion of 'logical friendliness', introduced into propositional logic in Makinson (2007). The result is a new conseque…
Robinson consistency in many-sorted hybrid first-order logics
Daniel Gaina, Guillermo Badia, Tomasz Kowalski
In this paper we prove a Robinson consistency theorem for a class of many-sorted hybrid logics as a consequence of an Omitting Types Theorem. An important corollary of this result…
Relevant Consequence Relations: An Invitation
Guillermo Badia, Petr Cintula, Libor Behounek +1
We generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance. The guiding idea follows the \emph{use criterion},…
A parametrised axiomatization for a large number of restricted second-order logics
Guillermo Badia, John Lane Bell
By limiting the range of the predicate variables in a second-order language one may obtain restricted versions of second-order logic such as weak second-order logic or definable su…
New foundations of reasoning via real-valued first-order logics
Guillermo Badia, Ronald Fagin, Carles Noguera
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in t…
Frame definability in finitely-valued modal logics
Guillermo Badia, Xavier Caicedo, Carles Noguera
In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot d…
Craig interpolation theorem fails in bi-intuitionistic predicate logic
Grigory K. Olkhovikov, Guillermo Badia
In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urqu…
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 logic without identity
Guillermo Badia, Xavier Caicedo, Carles Noguera
Lindström theorem obviously fails as a characterization of , first-order logic without identity. In this note we provide a fix: we show that $\mathcal{L}_{ωω…
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…
A Lindström theorem for intuitionistic propositional logic
Guillermo Badia, Grigory Olkhovikov
It is shown that propositional intuitionistic logic is the maximal (with respect to expressive power) abstract logic satisfying a certain topological property reminiscent of compac…
Saturated Models in Mathematical Fuzzy Logic
Guillermo Badia, Carles Noguera
This paper considers the problem of building saturated models for first-order graded logics. We define types as pairs of sets of formulas in one free variable which express propert…
On elimination of quantifiers in some non-classical mathematical theories
Guillermo Badia, Andrew Tedder
Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logica…
Infinitary propositional relevant languages with absurdity
Guillermo Badia
Analogues of Scott's isomorphism theorem, Karp's theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant log…
Fraisse classes of graded relational structures
Guillermo Badia, Carles Noguera
We study classes of graded structures satisfying the properties of amalgamation, joint embedding and hereditariness. Given appropriate conditions, we can build a graded analogue of…