Related papers: Graph-based Logic and Sketches
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
The presented work focuses on problems from determinant theory, set theory and topology. The term graph is the binding element that connects these problems. Graphs are distinguished by their geometrical simplicity, which helps in showing…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
Structured information about entities is critical for many semantic parsing tasks. We present an approach that uses a Graph Neural Network (GNN) architecture to incorporate information about relevant entities and their relations during…
Isomorphisms allow human cognition to transcribe a potentially unsolvable problem from one domain to a different domain where the problem might be more easily addressed. Current approaches only focus on transcribing structural information…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
Plural (or multiple-conclusion) cuts are inferences made by applying a structural rule introduced by Gentzen for his sequent formulation of classical logic. As singular (single-conclusion) cuts yield trees, which underlie ordinary natural…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
By designating vertices with variables, a simple undirected graph can be augmented to have an associated representing rational function in two variables taking the complex bi-upper halfplane to itself. We give relations between representing…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
We introduce a complete many-valued semantics for basic normal lattice-based modal logic. This relational semantics is grounded on many-valued formal contexts from Formal Concept Analysis. We discuss an interpretation and possible…
We continue work of our earlier paper (Lewitzka and Brunner: Minimally generated abstract logics, Logica Universalis 3(2), 2009), where abstract logics and particularly intuitionistic abstract logics are studied. Abstract logics can be…
The emergence of a variety of graph-based meaning representations (MRs) has sparked an important conversation about how to adequately represent semantic structure. These MRs exhibit structural differences that reflect different theoretical…
Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…
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…
In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…