In the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences of mathematical logic. There are several variations in the types of logical operation that can be used in these sentences.

You want to prove that some statement A is true. You can try to prove it directly, or you can prove it indirectly? we will show examples of each type of proof. Theorem: Every odd integer is the di erence of two perfect squares. (In other words, 8 odd integers x, 9y; z …

Apr 8, 2025 · Learn about matching in graphs, approximation algorithms, and optimization techniques. Explore graph colorings, chromatic numbers, and algorithms like Greedy Coloring for graph theory. Understand the basics of groups, subgroups, isomorphisms, and …

Dec 18, 2022 · In his papers on qualitative logic, entitative graphs, and existential graphs, Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.

We considers how a particular kind of graph corresponds to multiplica-tive intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication.

Dec 1, 2019 · How exactly does a logic of graphs differ from standard predicate logic? Here is an example from an article by Van Benthem: Definition 1 (P-graphs). Let L (P) be a propositional language built on the set of atoms P. A P-graph is a tuple G = …

Sep 21, 2021 · In this paper, we present and exemplify the Basic Graph Logic (BGL), this is an initial formalism which can be extended to provide a diagrammatic representation within which Set Theory and, hence, the whole of mathematics can be diagrammatic developed. We present the syntax, semantics, and inference engine of BGL.

Feb 8, 2018 · A logical graph is a graph-theoretic (http://planetmath.org/Graph) structure in one of the systems of graphical syntax that Charles Sanders Peirce developed for logic. In his papers on qualitative logic , entitative graphs , and existential graphs , Peirce developed several versions of a graphical formalism , or a graph-theoretic formal ...

For this reason, I will introduce graphs, and illustrate with examples how we can apply search & decision techniques to solve fundamental CAD problems. Subsequently, we will cover algorithms and their complexity issues.

Motivation: Logic is a fundamental building block of computation (e.g. digital circuits), and is also a very expressive language for encoding computational problems we want to solve. De nition 5.1 (informal).