Proofs as Graphs

Proofs as graphs

This note introduces a method of representing and reasoning about the actions of a class of proof procedures. A graph-like structure, called a proof diagram, is introduced in which conclusions of inferences can be shared. A version of Kruskal's Tree Theorem is developed for these structures and from there a notion of minimal proof is introduced. The notion of minimal proof allows us to make a l...

Proofs with Graphs

We present a graphical calculus, which allows mathematical formulae to be represented and reasoned about using a visual representation. We deene how a formula may be represented by a graph, and present a number of laws for transforming graphs, and describe the eeects these transformations have on the corresponding formulae. We then use these transformation laws to perform proofs. We illustrate ...

Functions as proofs as processes

This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the π-calculus closely related to linear logic. Decompositions of intuitionistic and classical logics into this system provide type-preserving translations of the λand λμ-calculus, both for call-by-name and call-by-value evaluation strategies. ...

Some Notes on Proofs with Alpha Graphs

It is well-known that Peirce’s Alpha graphs correspond to propositional logic (PL). Nonetheless, Peirce’s calculus for Alpha graphs differs to a large extent to the common calculi for PL. In this paper, some aspects of Peirce’s calculus are exploited. First of all, it is shown that the erasure-rule of Peirce’s calculus, which is the only rule which does not enjoy the finite choice property, is ...

Proofs as Games