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

Unintended Consequences From Nested State and Federal Regulations: The Case of the Pavley Greenhouse-gas-per-mile Limits

This paper reveals significant unintended consequences from recent 14-state efforts to reduce greenhouse gas emissions through limits on greenhouse gases per mile from new cars. We show that while such efforts significantly reduce emissions from new cars sold in the adopting states, they cause substantial emissions increases from new cars sold in other (non-adopting) states and from used cars. The costs per avoided ton of emissions are approximately twice as high once such offsets are recognized. Such offsets (or “leakage”) reflect interactions between the state-level initiatives and the federal fuel-economy standard: the state-level efforts effectively loosen the national standard, giving automakers scope to profitably increase sales of high-emissions automobiles in non-adopting states. Although the state-level efforts spur invention of fuel- and emissions-saving technologies, interactions with the federal standard limit the nationwide emissions reductions from such advances. Our multi-period simulation model estimates that a recent state-federal agreement avoids what would have been 74% leakage in the first phase of the state-level effort, and that potential for 65% leakage remains for the second phase. This research confronts a general issue of policy significance—namely, problems from “nested” state and federal environmental regulations. Similar leakage difficulties would arise under several newly proposed state-level initiatives

Hybrid sabotage modal logic

We introduce a new hybrid modal logic HSML for reasoning about sabotage-style graph games with edge deletions and provide a complete Hilbert-style axiomatization. We extend the completeness analysis to protocol models with restrictions on available edge deletions and clarify the connections between HSML-style logics of edge deletions and recent modal logics for stepwise point deletion from graphs

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

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

Symbolic Model Checking for Dynamic Epistemic Logic

Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, existing DEL implementations are ad-hoc, so we do not know how the framework really performs. For this purpose, we want to hook up with the best available model-checking and SAT techniques in computational logic. We do this by first providing a bridge: a new faithful representation of DEL models as so-called knowledge structures that allow for symbolic model checking. Next, we show that we can now solve well-known benchmark problems in epistemic scenarios much faster than with existing DEL methods. Finally, we show that our method is not just a matter of implementation, but that it raises significant issues about logical representation and update

Unintended Consequences from Nested State & Federal Regulations: The Case of the Pavley Greenhouse-Gas-per-Mile Limits

Fourteen U.S. states recently pledged to adopt limits on greenhouse gases (GHGs) per mile of light-duty automobiles. Previous analyses predicted this action would significantly reduce emissions from new cars in these states, but ignored possible offsetting emissions increases from policy-induced adjustments in new car markets in other (non-adopting) states and in the used car market. Such offsets (or “leakage”) reflect the fact that the state-level effort interacts with the national corporate average fuel economy (CAFE) standard: the state-level initiative effectively loosens the national standard and gives automakers scope to profitably increase sales of high-emissions automobiles in non-adopting states. In addition, although the state-level effort may well spur the invention of fuel- and emissions-saving technologies, interactions with the federal CAFE standard limit the nationwide emissions reductions from such advances. Using a multi-period numerical simulation model, we find that 70-80 percent of the emissions reductions from new cars in adopting states are offset by emissions leakage. This research examines a particular instance of a general issue of policy significance – namely, problems from “nested” federal and state environmental regulations. Such nesting implies that similar leakage difficulties are likely to arise under several newly proposed state-level initiatives.