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Andrew Tedder

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4 papers

2 author rows

FLAP Journal 2025 Journal Article

Some Polyadic Modal Boolean Algebras are Gaggles

Nicholas Ferenz
Andrew Tedder

J. Michael Dunn [4] introduced gaggle theory, which develops a close cor- respondence between certain kinds of algebras (called gaggles) and relational semantics. The gaggle framework has been applied to many propositional log- ics with much success. This paper is a foray into first-order logic via gaggle- theory. We show that monadic and polyadic Boolean algebras, introduced by Halmos [10] as algebraic structures to study first-order logic, are Boolean gaggles (in the sense of [3]), and that their extensions with certain kinds of operations are multi-gaggles. We show these algebraic structures to have representations in terms of, and embeddings in, relational semantics, using the gaggle-theoretic framework. That is, we employ relations to model all the operations, includ- ing those representing the quantifiers and variable substitutions. This project provides a foundation to explore first-order extensions of a wide range of logics. 2020 Mathematics Subject Classification. Primary: 03B45, Secondary: 03G15. ∗ NF acknowledges funding from by RVO 67985807 and that this work is also financed by national funds through FCT — Fundação para a Ciência e a Tecnologia, I. P. , under the scope of UIDB/00310/2020 project, identified as DOI 10. 54499/UIDB/00310/2020. † AT was funded by the DFG project TE 1611/1-1.

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LORI Conference 2021 Conference Paper

Situated Epistemic Updates

Igor Sedlár
Andrew Tedder

Abstract One way to model epistemic states of agents more realistically is to represent these states by sets of situations rather than possible worlds. In this paper we discuss representations of epistemic update in terms of situations. After linking epistemic update based on deleting epistemic accessibility arrows with update of situations, we discuss two specific kinds of public epistemic update; monotonic update in intuitionistic dynamic epistemic logic, and non-monotonic update in substructural dynamic epistemic logic. Our investigation is mainly conceptual, but leads to completeness results using reduction axioms, and lays the groundwork for future investigation into the concept of situated epistemic update.

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LORI Conference 2019 Conference Paper

First Degree Entailment with Group Attitudes and Information Updates

Igor Sedlár
Vít Puncochár
Andrew Tedder

Abstract We extend the epistemic logic with De Morgan negation by Fagin et al. (Artif. Intell. 79, 203–240, 1995) by adding operators for universal and common knowledge in a group of agents, and with a formalization of information update using a generalized version of the left division connective of the non-associative Lambek calculus. We provide sound and complete axiomatizations of the basic logic with the group operators and the basic logic with group operators and updates. Both logics are shown to be decidable.

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FLAP Journal 2017 Journal Article

Channel Composition and Ternary Relation Semantics.

Andrew Tedder

The focus of this paper is on the channel-theoretic interpretation given by Restall [19] as built on work by Barwise [2] in the framework of situation se- mantics. I characterise the notion of serial composition of channels, due to Barwise, and extend the ternary relation semantic framework to incorporate sets of points fitting the bill. It is shown that such an extension of the basic ternary relation semantic framework by such points is adequate for B∧, and so that restricting the class of B∧ models to those including composites is conser- vative over B∧. We close by noting directions for future research.

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