Reasoning and Modeling Paradigms Are Incompatible

Object-oriented and logic-programming paradigms are shown to be incompatible as component-based models of computation. This “impossibility result,” based on a new notion of observability of interactions among components, suggests that combining objectoriented with logic programming is not merely hard but impossible. It implies the more general incompatibility of reasoning and modeling and the impossibility reducing modeling to reasoning as in automatic program verification. While paradigmatic incompatibility is the most startling result of this paper, its novel use of models and meaics is of independently interest. The final sections introduce a notion of software complexity with parallels to computational complexity and a notion of “LP-completeness” that parallels NP-completeness. 1. Components, Reactiveness, and Encapsulation Deductive reasoning constrains problem solving so severely that it precludes flexible computational (or conceptual) modeling. This incompatibility, which depends on precise definitions of deductive reasoning and modeling, supports the intuition that logical people (and computers) are unadaptable and inflexible. The deductive reasoning paradigm (exemplified by logic programming) computes by proving theorems from axioms by rules of inference, while the modeling paradigm (exemplified by object-oriented programming) represents application domains (modeled worlds) so that their behavior can be described, predicted, and computed. Though reasoning and modeling paradigms are equivalent in “what” they can compute, they differ in “how” they organize computation. Reasoning paradigms view computation as “action-oriented” transformation (by instruction execution), while modeling paradigms view computation as “object-oriented” communication (among persistent software components). Differences between reasoning and modeling can also be expressed in terms of centralized versus distributed models of computation, or in terms of reduction (to subgoals) versus reaction (to stimuli). reasoning + action-oriented transformation + centralized -$ reductive distributed -+ reactive modeling + object-oriented communication + Incompatibility can be demonstrated by identifying any property possessed by one paradigm but not by the other. We demonstrate incompatibility in terms of a component-based model of computation: Definition: A model of computation is component-based if software components are the basic program unit and messages are the atomic unit of execution. Messages may in general have two kinds of effects: intemal effects (side-effects) that change a component’s state, and external effects on the environment. Though component-based models provide a framework for both modeling and reasoning paradigms, they clearly favor modeling at the expense of reasoning. We nevertheless choose component-based models as a basis for paradigm comparison because they are the preferred program structure for programming in the large, and because communication among components dominates computation within components for large, complex programs. Since modeling dominates reasoning for component-based models, logic (and mathematics) is a second-class form of component-based computation. This result balances the view, widely held by mathematicians, that computation is a second-class form of mathematics. The second-class status of logic (and mathematics) as a computational technique, taken together with the second-class status of computation as a mathematical technique, indicates that neither discipline dominates the other. The fundamental feature of modeling languages not possessed by reasoning languages is incremental adaptability. We focus on two forms of incremental adaptability, reactiveness and encapsulation, that respectively capture temporal and spatial incrementality: 115 0-8186-1060-3425/93 $03.00