Analytical Ontology: New Concepts of Representation

Although adequate ontology is an elementary requirement for theorising, scientific progress also depends crucially on the improvement of formal-analytical weaponry, such as mathematical representation or modelling techniques.

Advances in computing power have opened up entirely new possibilities for dealing with masses of data and information, and the computational sciences have provided an arsenal of new methods for analysing or modelling the complex phenomenon of eco­nomic change. The radical novelty of these developments lies not in the improvement of the received tools such as calculus, topology or descriptive statistics (which are all suit­able for the purposes of an analysis cast in a mechanistic mould) but, rather, in furnish­ing entirely new analytical tools and modelling techniques meeting the requirements of an evolutionary ontology.

The radical turn in analytical representation is well demonstrated by the fact that, in the computational sciences, this development is considered as being ontological, and in fact the term computational ontology is widely used nowadays. Various ontological issues have been surfacing in many of the works on analytical representation inspired by the digital age: e-science tools, computational automation and cyber-infrastructures (Kishore et al. 2004). Given the significance that ontology attains in this domain, we may assemble studies addressing computational and other kinds of analytical representation under the umbrella of analytical ontology.

Theoretical developments concurring with advances in analytical ontology abound. Multi-agent models have become standard for numerous special theoretical models (Grebel and Pyka 2006). An array of network models connects with multi-agent and related models highlighting the connective complexity (Potts 2000). Models featuring multidimensional fitness landscapes allow for the dynamic of differential adaptation and selection; path dependence and lock-in models posited in network structures have been designed to highlight the interconnectivities of non-ergodic paths (David 2005; Arthur 2013).

Models applying the (physics) synergy master equation have been introduced to give analytical precision to Veblen’s venerable proposition that there is circular causal­ity between individual and social behaviour (Weidlich 2000). Models featuring kernel density distribution methods have shed new light on the structure of income distribution, given dynamic knowledge differentials (Cantner et al., 2001).

Complexity economics has re-emerged from the 1950s as a general branch featuring new forms of analytical exposition, new tools and new modelling techniques (Arthur et al. 1997; Colander et al. 2010; Foster and Metcalfe 2012). Many of the analytical approaches have been producing offspring in the form of more special models, referring to particular theoretical problems (Kwasnicka and Kwasnicki 2006; Safarzynska and van den Bergh 2010).

The theoretical concept of rule has been specified analytically as requiring a deduc­tive format. For any rule R_j it holds that, “if condition C_j obtains, then operations Op” occur/are possible. While syllogism also applies to “laws” (as nomological rules), a rule in, for example, a classifier system has generic characteristics expounding variety, plas­ticity and evolvability. A special category inspired by biology deals with rules as genetic algorithms, adaptive genetic algorithms or hybrid genetic algorithms, paralleled by its sister branch of genetic programming.

Taking an overview, the contours of a unified programme may be seen to emerge in which analytical and semantic ontology combine - epitomised in the view of evolution as a form of computation (Beinhocker 2011).