This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...

Abstract: Qualitative reasoning is traditionally associated with the domain of physics, although the domain of application is, in fact, much broader. This paper investigates the application of qualitative reasoning beyond the domain of physics. It presents a case study of application in the social sciences: the density dependence theory of organizational ecology. It discusses how the different nature of soft science domains will complicate the process of model building. Furthermore, it shows that the “model building ” process can also help making theoretically important decisions, and, as a result, have an impact on the original theory. This will require a shift in focus from the “model simulation ” process towards the “model building ” process. 1

This article presents a formal reconstruction of James D. Thompson’s classic contribution to organization theory, Organizations in Action. The reconstruction explicates the underlying argumentation structure for Thompson’s propositions—literally, theorems or problems to be demonstrated. This allows Thompson’s propositions to be derived as theorems in a deductive theory. As it turns out, the formal theory is based on general assumptions using only few primitive concepts. In addition, this theory explains why Thompson’s propositions do not hold for noncomplex or “atomic ” organizations (a restriction on the domain of application). Furthermore, this study reveals that organizations attempt to reduce constraints in their environment—a heretofore unknown implication of the theory.

This paper provides practical operationalizations of criteria for evaluating scientific theories, such as the consistency and falsifiability of theories and the soundness of inferences, that take into account definitions. The precise formulation of these criteria is tailored to the use of automated theorem provers and automated model generators—generic tools from the field of automated reasoning. The use of these criteria is illustrated by applying them to a first order logic representation of a classic organization theory, Thompson’s Organizations in Action.

Scientific discourse leaves implicit a vast amount of knowledge, assumes that this background knowledge is taken into account—even taken for granted—and treated as undisputed. In particular, the terminology in the empirical sciences is treated as antecedently understood. The background knowledge surrounding a theory is usually assumed to be true or approximately true. This is in sharp contrast with logic, which explicitly ignores underlying presuppositions and assumes uninterpreted languages. We discuss the problems that background knowledge may cause for the formalization of scientific theories. In particular, we will show how some of these problems can be addressed in the context of the computational representation of scientific theories.

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