The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we o#er a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like FOL+K) in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. We conclude by o#ering a general completeness result for the entire family of first order classical modal logics (encompassing both normal and non-normal systems).

Abstract. The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like FOL + K) in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. Models of this type are either difficult of impossible to build in terms of relational Kripkean semantics. We conclude by introducing general first order neighborhood frames and we offer a general completeness result in terms of them which circumvents some well-known problems of propositional and first order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodified version of neighborhood frames). We argue that the semantical program that thus arises surpasses both in expressivity and adequacy the standard Kripkean approach, even when it comes to the study of first order normal systems.

A review of the literature on evaluating reasoning systems reveals that it is a very broad area with wide variation in depth and breadth of research on metrics and tests. Consolidation is hampered by nonstandard terminology, differing methodologies, scattered application domains, unpublished algorithmic details, and the effects of domain content and context on the choice of metric and tests. The field of information metrology, which applies to reasoning as a kind of information processing, is still emerging from ad hoc experience in evaluating narrow kinds of information systems. This report begins to bring order to the area by categorizing reasoning systems according to their capabilities. The characteristics of each category can be used as a basis for evaluating and testing reasoning systems claiming to be in that category. Capabilities are analyzed along several dimensions, including representation languages, inference, and user and software interfaces. The report groups representation languages by their relation to first-order logic, and model-theoretic properties, such as soundness and completeness. Inference procedures are divided into deduction, induction, abduction, and analogical reasoning. Capabilities of user and software interfaces are described as they apply to

Second-order logic and modal logic are both, separately, major topics of philosophical discussion. Although both have been criticized by Quine and others, increasingly many philosophers find their strictures uncompelling, and regard both branches of logic as valuable resources for the articulation and investigation of significant issues in logical metaphysics and elsewhere. One might therefore expect some combination of the two sorts of logic to constitute a natural and more comprehensive background logic for metaphysics. So it is somewhat surprising to find that philosophical discussion of secondorder modal logic is almost totally absent, despite the pioneering contribution of Barcan (1947). Two contrary explanations initially suggest themselves. One is that the topic of second-order modal logic is too hard: multiplying together the complexities of secondorder logic and of modal logic produces an intractable level of technical complication. 1 The other explanation is that the topic is too easy: its complexities are just those of second-order logic and of modal logic separately, combining which provokes no special further problems of philosophical interest. These putative explanations are less opposed