Related papers: The logic of vague categories
The primary goal of this paper is to recast the semantics of modal logic, and dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We first review the category of relations and categories of Kripke frames, with…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondene between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…
We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of…
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
The aim of illocutionary logic is to explain how context can affect the meaning of certain special kinds of performative utterances. Recall that performative utterances are understood as follows: a speaker performs the illocutionary act…
Modal dependence logics are modal logics defined on the basis of team semantics and have the downward closure property. In this paper, we introduce sound and complete deduction systems for the major modal dependence logics, especially those…
\textbf{T-BAT} logic is a formal system designed to express the notion of informal provability. This type of provability is closely related to mathematical practice and is quite often contrasted with formal provability, understood as a…
In this paper, firstly, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic L with partition function. Then, we investigate their position into the lattice of consequence relations over the language of…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
Modelling concept representation is a foundational problem in the study of cognition and linguistics. This work builds on the confluence of conceptual tools from G\"ardenfors semantic spaces, categorical compositional linguistics, and…
The paper proposes a new type of negation in multi-valued logics, providing a different way to answer the following question: what does it mean that some object language formula does not have a given truth-value. Along the way, the paper…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
Multi-valued functions are common in computable analysis (built upon the Type 2 Theory of Effectivity), and have made an appearance in complexity theory under the moniker search problems leading to complexity classes such as PPAD and PLS…