Intuitionistic Completeness of First-Order Logic

We establish completeness for intuitionistic first-order logic, iFOL, showing that is a formula is provable if and only if it is uniformly valid under the Brouwer Heyting Kolmogorov (BHK) semantics, the intended semantics of iFOL. Our proof is intuitionistic and provides an effective procedure Prf that converts uniform evidence into a formal first-order proof. We have implemented Prf . Uniform validity is defined using the intersection operator as a universal quantifier over the domain of discourse and atomic predicates. Formulas of iFOL that are uniformly valid are also intuitionistically valid, but not conversely. Our strongest result requires the Fan Theorem; it can also be proved classically by showing that Prf terminates using K¨onig’s Theorem. The fundamental idea behind our completeness theorem is that a single evidence term evd witnesses the uniform validity of a minimal logic formula F. Finding even one uniform realizer guarantees validity because Prf (F, evd) builds a first-order proof of F, establishing its uniform validity and providing a purely logical normalized realizer. We establish completeness for iFOL as follows. Friedman showed that iFOL can be embedded in minimal logic (mFOL). By his transformation, mapping formula A to F r(A). If A is uniformly valid, then so is F r(A), and by our Basic Completeness result, we can find a proof of F r(A) in minimal logic. Then we prove A from F r(A) in intuitionistic logic by a proof procedure fixed in advance. Our result resolves an open question posed by Beth in 1947

Generating event logics with higher-order processes as realizers

Our topic is broadening a practical ”proofs-as-programs” method of program development to “proofs-as-processes”. We extend our previous results that implement proofs-as-processes for the standard model of asynchronous message passing computation to a much wider class of process models including the ¼-calculus and other process algebras. Our first result is a general process model whose definition in type theory is interesting in itself both technically and foundationally. Process terms are type free lambda-terms. Typed processes are elements of a co-inductive type. They are higher-order in that they can take processes as inputs and produce them as outputs. A second new result is a procedure to generate event structures over the general process model and then define event logics and event classes over these structures. Processes are abstract realizers for assertions in the event logics over them, and they extend the class of primitively realizable propositions built on the propositions-as-types principle. They also provide a basis for the third new result, showing when programmable event classes generate strong realizers that prevent logical interference as processes are synthesized

Investigating correct-by-construction attack-tolerant systems

Attack-tolerant distributed systems change their protocols on-the-fly in response to apparent attacks from the environment; they substitute functionally equivalent versions possibly more resistant to detected threats. Alternative protocols can be packaged together as a single adaptive protocol or variants from a formal protocol library can be sent to threatened groups of processes. We are experimenting with libraries of attack-tolerant protocols that are correct-by-construction and testing them in environments that simulate specified threats, including constructive versions of the famous FLP imaginary adversary against fault-tolerant consensus. We expect that all variants of tolerant protocols are automatically generated and accompanied by machine checked proofs that the generated code satisfies formal properties.DARP

Open Bar - a Brouwerian Intuitionistic Logic with a Pinch of Excluded Middle

One of the differences between Brouwerian intuitionistic logic and classical logic is their treatment of time. In classical logic truth is atemporal, whereas in intuitionistic logic it is time-relative. Thus, in intuitionistic logic it is possible to acquire new knowledge as time progresses, whereas the classical Law of Excluded Middle (LEM) is essentially flattening the notion of time stating that it is possible to decide whether or not some knowledge will ever be acquired. This paper demonstrates that, nonetheless, the two approaches are not necessarily incompatible by introducing an intuitionistic type theory along with a Beth-like model for it that provide some middle ground. On one hand they incorporate a notion of progressing time and include evolving mathematical entities in the form of choice sequences, and on the other hand they are consistent with a variant of the classical LEM. Accordingly, this new type theory provides the basis for a more classically inclined Brouwerian intuitionistic type theory

Logic of Events, a framework to reason about distributed systems

We present a logical framework to reason about distributed systems called the Logic of Events. This logic has been formalized in Nuprl. We developed a suite of tools and tactics in Nuprl to reason about event classes. We also developed a programming language called EventML which allows programmers to write specifications of distributed protocols

Rapid Stereomicroscopic Imaging of HER2 Overexpression in Ex Vivo Breast Tissue Using Topically Applied Silica-Based Gold Nanoshells

Tumor margin detection for patients undergoing breast conservation surgery primarily occurs postoperatively. Previously, we demonstrated that gold nanoshells rapidly enhance contrast of HER2 overexpression in ex vivo tissue sections. Our ultimate objective, however, is to discern HER2 overexpressing tissue from normal tissue in whole, nonsectioned, specimens to facilitate rapid diagnoses. Here, we use targeted nanoshells to quickly and effectively visualize HER2 receptor expression in intact ex vivo human breast tissue specimens. Punch biopsies of human breast tissue were analyzed after a brief 5-minute incubation with and without HER2-targeted silica-gold nanoshells using two-photon microscopy and stereomicroscopy. Labeling was subsequently verified using reflectance confocal microscopy, darkfield hyperspectral imaging, and immunohistochemistry to confirm levels of HER2 expression. Our results suggest that anti-HER2 nanoshells used in tandem with a near-infrared reflectance confocal microscope and a standard stereomicroscope may potentially be used to discern HER2-overexpressing cancerous tissue from normal tissue in near real time and offer a rapid supplement to current diagnostic techniques

U-Pb Studies of Zircon Cores and Overgrowths, and Monazite: Implications for Age and Petrogenesis of the Northeastern Idaho Batholith

U/Pb isotopic studies of zircons, many containing xenocrystic cores with euhedral overgrowths, and monazite from igneous rocks and metasedimentary inclusions of the northeastern Idaho batholith yield linear arrays on concordia diagrams. We interpret these as mixing lines between an old component (cores) and a young component (overgrowths and zircons without cores). The lower intercept of such arrays with concordia may yield the minimum age of the rocks if the overgrowths and zircons without cores are discordant, or the crystallization age if they are concordant. Monazites yield apparently concordant ages either equal or less than the lower intercept zircon ages. The samples studied yield lower intercept ages ranging from 73.5+ or -6 Ma (foliated quartz diorite) to 46.5+ or -1 Ma (feldspar megacryst granite); ages obtained are consistent with crosscutting relations observed in the field. Upper intercepts yield ages of 1700 to 2349 Ma. These are interpreted to indicate the mean age of xenocrystic zircon. Studies of zircons from xenolith suites indicate that they could represent the source of the old zircon component. The zircon and monazite results, the generally high initial 87Sr/86Sr ratios of the igneous rocks, and the isotopic composition of Pb in feldspar indicate that the magmas were derived anatectically from a continental crustal source or were extensively mixed with such old crust prior to or during emplacement

The Global Health and Care Worker Compact: Evidence Base and Policy Considerations

Background During the COVID-19 pandemic, and recognising the sacrifice of health and care workers alongside discrimination, violence, poor working conditions and other violations of their rights, health and safety, in 2021 the World Health Assembly requested WHO to develop a global health and care worker compact, building on existing normative documentation, to provide guidance to ‘protect health and care workers and safeguard their rights’. Methods A review of existing international law and other normative documents was conducted. We manually searched five main sets of international instruments: (1) International Labour Organization conventions and recommendations; (2) WHO documents; (3) United Nations (UN) human rights treaties and related documents; (4) UN Security Council and General Assembly resolutions and (5) the Geneva Conventions and Additional Protocols. We included only legal or other normative documents with a global or regional focus directly addressing or relevant to health and care workers or workers overall. Results More than 70 documents met our search criteria. Collectively, they fell into four domains, within which we identified 10 distinct areas: (1) preventing harm, encompassing (A) occupational hazards, (B) violence and harassment and (C) attacks in situations of fragility, conflict and violence; (2) inclusivity, encompassing (A) non-discrimination and equality; (3) providing support, encompassing (A) fair and equitable remuneration, (B) social protection and (C) enabling work environments and (4) safeguarding rights, encompassing (A) freedom of association and collective bargaining and (B) whistle-blower protections and freedom from retaliation. Discussion A robust legal and policy framework exists for supporting health and care workers and safeguarding their rights. Specific human rights, the right to health overall, and other binding and non-binding legal documents provide firm grounding for the compact. However, these existing commitments are not being fully met. Implementing the compact will require more effective governance mechanisms and new policies, in partnership with health and care workers themselves