Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi

Thou Shalt is not You Will

In this paper we discuss some reasons why temporal logic might not be suitable to model real life norms. To show this, we present a novel deontic logic contrary-to-duty/derived permission paradox based on the interaction of obligations, permissions and contrary-to-duty obligations. The paradox is inspired by real life norms

Pilot Situation Awareness and Risk of Critical Incidents Using a Novel Online Flight Simulation Tool

Pilot situation awareness (SA) is a critical influence on decision making and an important element in maintaining the safe control of an aircraft. The present research investigated whether measures of pilot SA, gathered via an online computer-based cognitive screening tool for pilots, could be used to predict pilot’s likelihood of real-world critical incidents. A risk score for each pilot was developed based on their self-reported critical incidents from their actual flight history. It was hypothesized that individuals with lower SA scores would have higher risk scores. The impact of age and pilot experience were also considered, as these factors are known to influence achievement of SA. Results report on comprehensive models of flight performance that quantify the effects of three levels of SA on risk

Consolidation of Belief in Two Logics of Evidence

Recently, several logics have emerged with the goal of modelling evidence in a more relaxed sense than that of justifications. Here, we explore two of these logics, one based on neighborhood models and the other being a four-valued modal logic. We establish grounds for comparing these logics, finding, for any model, a counterpart in the other logic which represents roughly the same evidential situation. Then we propose operations for consolidation, answering our central question: What should the doxastic state of a rational agent be in a given evidential situation? These operations map evidence models to Kripke models. We then compare the consolidations in the two logics, finding conditions under which they are isomorphic. By taking this dynamic perspective on belief formation we pave the way for, among other things, a study of the complexity, and an AGM-style analysis of rationality of these belief-forming processes