# Wesley FussnerUniversität Bern | UniBe · Mathematical Institute

Wesley Fussner

Doctor of Philosophy

## About

19

Publications

678

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77

Citations

Introduction

I'm currently a postdoctoral scholar at the University of Bern, where my research is primarily in algebraic logic and duality theory. I also actively use tools from automated theorem proving in my work.

**Skills and Expertise**

## Publications

Publications (19)

We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transpo...

We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and generalizes two semantics already appearing in the literature: Aguzzoli, Bianchi, and Marra’s temporal flow semanti...

We give a structural decomposition of conic idempotent residuated lattices, showing that each of them is an ordinal sum of certain simpler partially ordered structures. This ordinal sum is indexed by a totally ordered residuated lattice, which serves as its skeleton and is both a subalgebra and nuclear image, and we equationally characterize which...

We show that under certain conditions, well-studied algebraic properties transfer from the class $\mathcal{V}_{_\text{FSI}}$ of finitely subdirectly irreducible members of a variety $\mathcal{V}$ to the whole variety, and, in certain cases, back again. First, we prove that a congruence-distributive variety $\mathcal{V}$ has the congruence extension...

We introduce a family of modal expansions of Łukasiewicz logic that are designed to accommodate modal translations of generalized basic logic (as formulated with exchange, weakening, and falsum). We further exhibit algebraic semantics for each logic in this family, in particular showing that all of them are algebraizable in the sense of Blok and Pi...

We propose an approach for searching for counterexamples of statements about algebraic structures with a medium-sized signature using the Isabelle proof assistant in an efficient, parallel manner. We contribute a Python client Isabelle server and other scripts implementing our approach, and provide results of our computational experiments. In parti...

We introduce a family of modal expansions of {\L}ukasiewicz logic that are designed to accommodate modal translations of generalized basic logic (as formulated with exchange, weakening, and falsum). We further exhibit algebraic semantics for each logic in this family, in particular showing that all of them are algebraizable in the sense of Blok and...

We introduce residuated ortholattices as a generalization of--and environment for the investigation of--orthomodular lattices. We establish a number of basic algebraic facts regarding these structures, characterize orthomodular lattices as those residuated ortholattices whose residual operation is term-definable in the involutive lattice signature,...

We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of th...

We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and generalizes two semantics already appearing in the literature: Aguzzoli, Bianchi, and Marra's temporal flow semanti...

We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of th...

In residuated binars there are six non-obvious distributivity identities of ·,/,\\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cdot ,/,\backslash $$\end{document} ov...

We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as (possibly partial) functions. Providing a partial answer to a question of Gehrke, we demonstrate that functionality i...

We give a dualized construction of Aguzzoli–Flaminio–Ugolini of a large class of MTL-algebras from quadruples \((\mathbf{B},\mathbf{A},\vee _e,\delta )\), consisting of a Boolean algebra \(\mathbf{B}\), a generalized MTL-algebra \(\mathbf{A}\), and maps \(\vee _e\) and \(\delta \) parameterizing the connection between these two constituent pieces....

In residuated binars there are six non-obvious distributivity identities of $\cdot$,$/$,$\backslash$ over $\wedge, \vee$. We show that in residuated binars with distributive lattice reducts there are some dependencies among these identities; specifically, there are six pairs of identities that imply another one of these identities, and we provide c...

We dualize a construction of Aguzzoli-Flaminio-Ugolini of a large class of MTL-algebras from ordered quadruples consisting of a Boolean algebra, a generalized MTL-algebra, and two maps parameterizing the connection between these pieces. Our dualized construction gives a uniform way of building the extended Priestley duals of MTL-algebras in this cl...

In this paper, we investigate the asymptotic behavior of the Benjamin–Bona–Mahony equation in unbounded domains. We prove the existence of a global attractor when the equation is defined in a three-dimensional channel. The asymptotic compactness of the solution operator is obtained by the uniform estimates on the tails of solutions.

## Projects

Project (1)

This is a line of research started in 2009 and aimed at understanding the phenomenon of Sahlqvist correspondence and canonicity from an algebraic viewpoint. Thanks to Stone-type dualities, we have been able to reformulate the Sahlqvist mechanism in terms of the order-theoretic properties of the algebraic interpretation of the logical connectives. In its turn, this order-theoretic reformulation has made it possible to extend the state-of-the-art in Sahlqvist theory from classical normal modal logic to classes of logics algebraically captured by normal and regular (distributive) lattice expansions, mu calculi, hybrid logics, and many valued logics.