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Qualitative Models in Computational Simulative Sciences: Representation, Confirmation, Experimentation

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Abstract

The Epistemology Of Computer Simulation (EOCS) has developed as an epistemological and methodological analysis of simulative sciences using quantitative computational models to represent and predict empirical phenomena of interest. In this paper, Executable Cell Biology (ECB) and Agent-Based Modelling (ABM) are examined to show how one may take advantage of qualitative computational models to evaluate reachability properties of reactive systems. In contrast to the thesis, advanced by EOCS, that computational models are not adequate representations of the simulated empirical systems, it is shown how the representational adequacy of qualitative models is essential to evaluate reachability properties. Justification theory, if not playing an essential role in EOCS, is exhibited to be involved in the process of advancing and corroborating model-based hypotheses about empirical systems in ECB and ABM. Finally, the practice of evaluating model-based hypothesis by testing the simulated systems is shown to constitute an argument in favour of the thesis that computer simulations in ECB and ABM can be put on a par with scientific experiments.

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  1. Computational models in ABM are usually identified with the simulative programs which, by assigning different values to the program’s variables, can be acknowledged as quantitative models. Section 2.2 will nonetheless consider computational models in ABM to be models of the simulative programs which, as it will be extensively shown, are qualitative in nature.

  2. This categorization is taken from Brim et al. (2013).

  3. Other kinds of computational models include continuous-time and discrete-time Markov chains (Yang and Ko 2012), characterized by discrete variables, stochastic rules and, respectively, continuous or discrete time. One reason to focus on purely qualitative models such as KSs is that, at the state of the art, they allow for a better analysis of their state space and therefore most of current research in ECB focuses on them.

  4. Temporal logics express how systems evolve over time and are interpreted over state transition systems. LTL assumes that time is linear, that is, at each state, only one successor state is considered.

  5. This known fact led some, especially Winsberg (2010), to argue that the processes of verification and validation, although conceptually distinct, cannot always be distinguished in the practice of computer simulations.

  6. CTL and CTLK assume that time has a branching structure: at each state (instant of time), distinct computational paths are considered. This is expressed using path quantifiers in CTL and CTLK formulas, requiring that the given statement holds in all paths (A) or in at least one path (E) starting from some specified or initial state.

  7. In connection with agent-based models expressed as reactive systems, simulation becomes necessary for exploratory purposes, i.e. when one observes the running program to detect behaviours of interest but no advanced hypotheses have to be evaluated.

  8. Given a set \(i \in \{ 1,...,n \}\) of agents, a model T for the n agents is introduced as the set-theoretic structure \((S, \pi , P_i, P_n)\) defined by a set S of states denoting possible worlds for agents; an interpretation function \(\pi\) mapping, for each \(s \in S\), from a set of proposition \(\Phi\) to truth values and describing each possible world; a binary relation \(P_i \subseteq S \times S\) defined for states in S and for each agent \(1 \le i \le n\). \(P_i = (s_i, s_j)\) is the possibility relation expressing that agent i considers world \(s_j\) as possible on the basis of the knowledge she possesses at world \(s_i\), for any \(s_i, s_j \in S\). The environment is often modelled as an agent \(n + 1\) outside the set 1, ..., n of agents (Fagin et al. 2004, ch. 4).

    The possibility relation \(P_i\) allows KSs for agent-based models to provide an interpretation for the epistemic operator \(K_i\). \(K_i \phi\) holds true iff agent i regards proposition \(\phi\) to be true in all worlds she considers possible. Given a KS T, a world \(s_i\), and a formula f, \(T, s_i \models f\) means that f is satisfied by structure T at world \(s_i\). The semantics for the \(K_i\) operator can thus be formally given as: \((T, s_i) \models K_i f\) iff \((T, s_j) \models f\) for all \((s_i, s_j) \in P_i.\)

  9. It is a discussed topic in the debate on the philosophical novelty of computer simulations whether the problem of maximizing trading-off properties also characterises scientific modelling. For instance, the philosophical analysis of idealization in science deals, among other things, with the problem of maximizing simplicity and precision in scientific models (Weisberg 2007).

  10. In the context of the philosophy of computer science, it has been even argued that the representational relation holding between a KS and the specified program is that of empirical adequacy as understood by Van Fraassen (1980) (Angius and Tamburrini 2011).

  11. Measurement as well as other epistemological and methodological problems affecting experiments are not discussed here in that they are common to any scientific experiment and they have been deeply analysed by the epistemology of scientific experiments (Franklin 1990).

  12. The problem of whether there are pure exploratory experiments in science, that is, experiments carried out without any theoretical presupposition, is object of philosophical debate in the epistemology of scientific experiments (Franklin 1989). Here, scientific experiments are taken to be theory-laden at least in the weaker sense of theory-guidance proposed by (Godfrey-Smith 2009, ch. 5), namely when there exists a theory that guides the experiments in choosing which elements of the experimented system to observe.

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  1. Department of History, Human Sciences, and Education, University of Sassari, Sassari, Italy

    Nicola Angius

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Angius, N. Qualitative Models in Computational Simulative Sciences: Representation, Confirmation, Experimentation. Minds & Machines 29, 397–416 (2019). https://doi.org/10.1007/s11023-019-09503-9

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