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

Betahistine in Meniere's disease or syndrome: a systematic review

Background: Meniere's disease is characterized by recurrent episodes of vertigo, hearing loss, and tinnitus, often with a feeling of fullness in the ear. Although betahistine is thought to be specifically effective for Meniere's disease, no evidence for a benefit from the use of betahistine exists, despite its widespread use. Reassessment of the effect of betahistine for Meniere's disease is now warranted. Search Methods: We searched for randomized controlled trials (RCTs) in the Central Register of Controlled Trials (CENTRAL), Ovid Medline, Ovid Embase, CINAHL, Web of Science, Clinicaltrials.gov, ICTRP, and additional sources for published and unpublished trials, in which betahistine was compared to placebo. Data Collection and Analysis: Our outcomes involved vertigo, significant adverse effect (upper gastrointestinal discomfort), hearing loss, tinnitus, aural fullness, other adverse effects, and disease-specific health-related quality of life. We used GRADE to assess the quality of the evidence. Main Results: We included 10 studies: 5 studies used a crossover design and the remaining 5 were parallel-group RCTs. One study with a low risk of bias found no significant difference between the betahistine groups and placebo with respect to vertigo after a long-term follow-up period. No significant difference in the incidence of upper gastrointestinal discomfort was found in 2 studies (low-certainty evidence). No differences in hearing loss, tinnitus, or well-being and disease-specific health-related quality of life were found (low- to very low-certainty of evidence). Data on aural fullness could not be extracted. No significant difference between the betahistine and the placebo groups (low-certainty evidence) could be demonstrated in the other adverse effect outcome with respect to dull headache. The pooled risk ratio for other adverse effect in the long term demonstrated a lower risk in favor of placebo over betahistine. Conclusions: High-quality studies evaluating the effect of betahistine on patients with Meniere's disease are lacking. However, one study with low risk of bias found no evidence of a difference in the effect of betahistine on the primary outcome, vertigo, in patients with Meniere's disease when compared to placebo. The main focus of future research should be on the use of comparable outcome measures by means of patient-reported outcome measures.Disorders of the head and nec

Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model

Heifetz, Meier and Schipper (HMS) present a lattice model of awareness. The HMS model is syntax-free, which precludes the simple option to rely on formal language to induce lattices, and represents uncertainty and unawareness with one entangled construct, making it difficult to assess the properties of either. Here, we present a model based on a lattice of Kripke models, induced by atom subset inclusion, in which uncertainty and unawareness are separate. We show the models to be equivalent by defining transformations between them which preserve formula satisfaction, and obtain completeness through our and HMS' results.Comment: 18 pages, 2 figures, proceedings of DaLi conference 202

Constructive Hybrid Games

Hybrid games are models which combine discrete, continuous, and adversarial dynamics. Game logic enables proving (classical) existence of winning strategies. We introduce constructive differential game logic (CdGL) for hybrid games, where proofs that a player can win the game correspond to computable winning strategies. This is the logical foundation for synthesis of correct control and monitoring code for safety-critical cyber-physical systems. Our contributions include novel static and dynamic semantics as well as soundness and consistency.Comment: 60 pages, preprint, under revie