Aristotelian Syntax from a Computational–Combinatorial Point of View

Abstract

This paper translates Aristotelian logic into the sphere of computational-combinatorical research methods. The task is accomplished by formalising Aristotle's logical system in terms of rule-based reduction relations on a suitable basic set, which allow us to apply standard concepts of the theory of such structures (Newman lemma) to the ancient logical system. In this way we are able to reproduce Aristotle's method of deriving syllogisms within a precisely dened formal environment, and we can analyse the structure of the set of syllogistic rules by means of a computer program. Thus we show that Aristotle's syllogistic logic is a formal system of its own, which can be modelled independently of predicate logic and set theory. Our research is very much in the spirit of Smiley's and Corcoran's modelling of Aristotelian logic as a deductional system, and we aim to staying close to Aristotle's own termlogical concepts.

DOMINO – An Efficient Algorithm for Policy Definition and Processing in Distributed Environments Based on Atomic Data Structures

“…If a new proposition is already included in the set of existing premises, it is not added as a new premise; the iteration process ends if no new propositions are found. While [6] describes a computational syllogism web page implemented on a php server, we have implemented our own DOMINO reasoner in pure Javascript. The implementation has a small footprint, does not depend on server side computing and can be run in any browser (even as local html file) or used as a library for W3C or other HTML widgets or apps for the WAC [9] runtime, the Firefox OS or Google Chrome.…”

“…In our DOMINO system, the bricks correspond to term logic premises, where each premise is composed of two terms (subject and predicate). Like with the domino game, bricks are linked according to syllogistic rules [10], which can be computed by software [6].…”

“…Note that matching of two expressions can be defined in different ways, e.g numbers checked for equality or matching strings (as used in [6]). In DOMINO, we opt for flexibility and allow numbers to be compared, or being matched with intervals or "<" and ">" relations, while strings could be matched using regular expressions.…”

“…In order to achieve these goals, we have designed and implemented a reasoning system and language based on (Aristotelian) term logic [6] which has experienced a revival since the 1970s, mainly due to the constant criticism that predicate logic is unnatural as its syntax does not follow the one used in people's everyday reasoning. Also in the field of artificial intelligence it has gained momentum, e.g.…”

An Intensional Leibniz Semantics for Aristotelian Logic

“…It was his idea to use pairs of numbers which has lead us to the general construction of a set theoretical intensional model of Aristotelian logic. Leibniz of course did not put his ideas into the modern framework of syntax/semantics interplay of the Tarski type, as we will do, but in hindsight it has been a big step in that direction (Glashoff, 2002).…”