1,243 research outputs found
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
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
- …