Connexive implication

This paper contains a rigorous treatment of the species of implication described in [8] and [9], where it was given the name of connexive implication. A brief historical survey will lay bare its roots in antiquity, and it will be shown that none of the well-known systems of propositional logic serves to formalize it.1 In this paper a new system of ‘connexive’ logic will be presented, the system being shown to be (a) consistent, (b) independent of two-valued logic, (c) Post-complete.

Download Full-text

Large-Size Message Construction for ETI: Self-Interpretation in LINCOS

Symposium - International Astronomical Union ◽

10.1017/s0074180900193787 ◽

2004 ◽

Vol 213 ◽

pp. 499-504 ◽

Cited By ~ 1

Author(s):

Alexander Ollongren ◽

Douglas A. Vakoch

Keyword(s):

Propositional Logic ◽

Constructive Logic ◽

Minimal Set ◽

Natural Languages ◽

Abstract System ◽

System A ◽

Large Size ◽

Meta Level ◽

New System ◽

Considerable Size

Messages for ETI written in a terrestrial language admitting linear notation, should be supplied with extra-linguistic annotations – also linearized in some way – as an aid for interpretation by recipients. In several papers the first author has advocated the use at the second level of an abstract system (a new Lingua Cosmica, still under development), based on constructive logic – with a minimal set of primitives. Expressions at the meta level explain the logic contents of messages.The interaction between any LINCOS and text may suffice for interpretation of both – provided the messages and annotations are of considerable size. Finding a measure for the sizes involved is, however, a non-trivial problem. As a result, one is interested in methods for interpreting a LINCOS without recourse to natural languages. The present paper is concerned with the problem of interpretation of the new system within itself. For that purpose, interpretation of parts of it and (complete) propositional logic in terms of each other is considered (commutativity). This leads to self-interpretation as all semantic terms reside in the closed context of the system.

Download Full-text