
59What Is an Inconsistent Truth Table?Australasian Journal of Philosophy 94 (3): 533548. 2016.ABSTRACTDo truth tables—the ordinary sort that we use in teaching and explaining basic propositional logic—require an assumption of consistency for their construction? In this essay we show that truth tables can be built in a consistencyindependent paraconsistent setting, without any appeal to classical logic. This is evidence for a more general claim—that when we write down the orthodox semantic clauses for a logic, whatever logic we presuppose in the background will be the logic that appears …Read more

38BiSimulating in BiIntuitionistic LogicStudia Logica 104 (5): 10371050. 2016.Biintuitionistic logic is the result of adding the dual of intuitionistic implication to intuitionistic logic. In this note, we characterize the expressive power of this logic by showing that the ﬁrst order formulas equivalent to translations of biintuitionistic propositional formulas are exactly those preserved under biintuitionistic directed bisimulations. The proof technique is originally due to Lindstrom and, in contrast to the most common proofs of this kind of result, it does not use th…Read more

29The relevant fragment of first order logicReview of Symbolic Logic 9 (1): 143166. 2016.Under a proper translation, the languages of propositional (and quantified relevant logic) with an absurdity constant are characterized as the fragments of first order logic preserved under (worldobject) relevant directed bisimulations. Furthermore, the properties of pointed models axiomatizable by sets of propositional relevant formulas have a purely algebraic characterization. Finally, a form of the interpolation property holds for the relevant fragment of first order logic.

19A Lindströmstyle theorem for finitary propositional weak entailment languages with absurdityLogic Journal of the IGPL 24 (2): 115137. 2016.Following a result by De Rijke for modal logic, it is shown that the basic weak entailment modeltheoretic language with absurdity is the maximal modeltheoretic language having the finite occurrence property, preservation under relevant directed bisimulations and the finite depth property. This can be seen as a generalized preservation theorem characterizing propositional weak entailment formulas among formulas of other modeltheoretic languages.

17Syntactic characterizations of ﬁrstorder structures in mathematical fuzzy logicSoft Computing. forthcoming.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 syntactic form of their firstorder axiomatization. We focus on classes given by universal and universalexistential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTLalgebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–S…Read more

16Infinitary propositional relevant languages with absurdityReview of Symbolic Logic 10 (4): 663681. 2017.

13Currying Omnipotence: A Reply to Beall and CotnoirThought: A Journal of Philosophy 7 (2): 119121. 2018.

11A traditional aspect of model theory has been the interplay between formal languages and mathematical structures. This dissertation is concerned, in particular, with the relationship between the languages of relevant logic and RoutleyMeyer models. One fundamental question is treated: what is the expressive power of relevant languages in the RoutleyMeyer framework? In the case of finitary relevant propositional languages, two answers are provided. The first is that finitary propositional releva…Read more

7On elimination of quantifiers in some nonclassical mathematical theoriesMathematical Logic Quarterly 64 (3): 140154. 2018.

6A Lindström Theorem in ManyValued Modal Logic over a Finite MTLchainFuzzy Sets and Systems. forthcoming.We consider a modal language over crisp frames and formulas evaluated on a finite MTLchain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTLchain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property.

6On Sahlqvist Formulas in Relevant LogicJournal of Philosophical Logic 47 (4): 673691. 2018.This paper defines a Sahlqvist fragment for relevant logic and establishes that each class of frames in the RoutleyMeyer semantics which is definable by a Sahlqvist formula is also elementary, that is, it coincides with the class of structures satisfying a given first order property calculable by a Sahlqvistvan Benthem algorithm. Furthermore, we show that some classes of RoutleyMeyer frames definable by a relevant formula are not elementary.

4Variable Sharing in Substructural Logics: An Algebraic CharacterizationBulletin of the Section of Logic 47 (2): 107115. 2018.We characterize the nontrivial substructural logics having the variable sharing property as well as its strong version. To this end, we find the algebraic counterparts over varieties of these logical properties.

3A Remark on Maksimova's Variable Separation Property in SuperBiIntuitionistic LogicsAustralasian Journal of Logic 14 (1). 2017.We provide a sucient frametheoretic condition for a super biintuitionistic logic to have Maksimova's variable separation property. We conclude that biintuitionistic logic enjoys the property. Furthermore, we offer an algebraic characterization of the superbiintuitionistic logics with Maksimova's property.

Fraïssé classes of graded relational structuresTheoretical Computer Science 737. 2018.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 the Fraïssé limit. Some examples such as the class of all finite weighted graphs or the class of all finite fuzzy orders (evaluated on a particular countable algebra) will be examined.

Model definability in relevant logicIfCoLog Journal of Logics and Their Applications 3 (4): 623646. 2017.It is shown that the classes of RoutleyMeyer models which are axiomatizable by a theory in a propositional relevant language with fusion and the Ackermann constant can be characterized by their closure under certain modeltheoretic operations involving prime filter extensions, relevant directed bisimulations and disjoint unions.

A Lindström theorem for intuitionistic propositional logicNotre Dame Journal of Formal Logic. forthcoming.It is shown that propositional intuitionistic logic is the maximal (with respect to expressive power) abstract logic satisfying a certain topological property reminiscent of compactness, the Tarski union property and preservation under asimulations.
Brisbane, Queensland, Australia
Areas of Specialization
Logic and Philosophy of Logic 
Philosophy of Mathematics 
Areas of Interest
Logic and Philosophy of Logic 
Philosophy of Mathematics 