Superdeduction in Lambda-Bar-Mu-Mu-Tilde

Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term language and a cut-elimination reduction already exist for superdeduction, both based on Christian Urban's work on classical sequent calculus. However the computational content of Christian Urban's calculus is not directly related to the (lambda-calculus based) Curry-Howard correspondence. In contrast the Lambda bar mu mu tilde calculus is a lambda-calculus for classical sequent calculus. This short paper is a first step towards a further exploration of the computational content of superdeduction proofs, for we extend the Lambda bar mu mu tilde calculus in order to obtain a proofterm langage together with a cut-elimination reduction for superdeduction. We also prove strong normalisation for this extension of the Lambda bar mu mu tilde calculus.Comment: In Proceedings CL&C 2010, arXiv:1101.520

Orthogonality and Boolean Algebras for Deduction Modulo

Originating from automated theorem proving, deduction modulo removes computational arguments from proofs by interleaving rewriting with the deduction process. From a proof-theoretic point of view, deduction modulo defines a generic notion of cut that applies to any first-order theory presented as a rewrite system. In such a setting, one can prove cut-elimination theorems that apply to many theories, provided they verify some generic criterion. Pre-Heyting algebras are a generalization of Heyting algebras which are used by Dowek to provide a semantic intuitionistic criterion called superconsistency for generic cut-elimination. This paper uses pre-Boolean algebras (generalizing Boolean algebras) and biorthogonality to prove a generic cut-elimination theorem for the classical sequent calculus modulo. It gives this way a novel application of reducibility candidates techniques, avoiding the use of proof-terms and simplifying the arguments

Three Dimensional Proofnets for Classical Logic

Classical logic and more precisely classical sequent calculi are currently the subject of several studies that aim at providing them with an algorithmic meaning. They are however ruled by an annoying syntactic bureaucracy which is a cause of pathologic non-confluence. An interesting patch consists in representing proofs using proofnets. This leads (at least in the propositional case) to cut-elimination procedures that remain confluent and strongly normalising without using any restricting reduction strategy. In this paper we describe a presentation of sequents in a two-dimensional space as well as a presentation of proofnets and sequent calculus derivations in a three-dimensional space. These renderings admit interesting geometrical properties: sequent occurrences appear as parallel segments in the case of three-dimensional sequent calculus derivations and the De Morgan duality is expressed by the fact that negation stands for a ninety degree rotation in the case of two-dimensional sequents and three-dimensional proofnets

Axiom directed Focusing

Long versionInternational audienceSuperdeduction and deduction modulo are methods specially designed to ease the use of first-order theories in predicate logic. Superdeduction modulo, which combines both, enables the user to make a distinct use of computational and reasoning axioms. Although soundness is ensured, using superdeduction and deduction modulo to extend deduction with awkward theories can jeopardize essential properties of the extended system such as cut-elimination or completeness \wrt~predicate logic. Therefore one has to design criteria for theories which can safely be used through superdeduction and deduction modulo. In this paper we revisit the superdeduction paradigm by comparing it with the focusing approach. In particular we prove a focalization theorem for cut-free superdeduction modulo: we show that permutations of inference rules can transform any cut-free proof in deduction modulo into a cut-free proof in superdeduction modulo and conversely, provided that some hypotheses on the synchrony of reasoning axioms are verified. It implies that cut-elimination for deduction modulo and for superdeduction modulo are equivalent. Since several criteria have already been proposed for theories that do not break cut-elimination of the corresponding deduction modulo system, these criteria also imply cut-elimination of the superdeduction modulo system, provided our synchrony hypotheses hold. Finally we design a tableaux method for superdeduction modulo which is sound and complete provided cut-elimination holds

Case Report: Concomitant Diagnosis of Plasma Cell Leukemia in Patient With JAK2 Positive Myeloproliferative Neoplasm.

Plasma cell dyscrasias and myeloproliferative neoplasms (MPN) are hematologic malignancies arising from two distinct hematopoietic cell lineages. They rarely occur concomitantly. Here, we report a case of a patient with a recent diagnosis of a JAK2 V617F positive MPN who presented with a new diagnosis of plasma cell leukemia. The patient had presented to the hospital with a leukocytosis predominantly comprised of plasma cells, followed by work-up involving peripheral blood flow cytometry, FISH analysis, and bone-marrow biopsy. FISH analysis was suggestive of a common progenitor cell for these distinct hematologic malignancies. To our knowledge, this case represents the second reported instance of a concomitant JAK2 positive MPN with primary plasma cell leukemia

Strong Normalization in two Pure Pattern Type Systems

International audiencePure Pattern Type Systems (P 2 T S ) combine in a unified setting the frameworks and capabilities of rewriting and λ-calculus. Their type systems, adapted from Barendregt's λ-cube, are especially interesting from a logical point of view. Strong normalization, an essential property for logical soundness, had only been conjectured so far: in this paper, we give a positive answer for the simply-typed system and the dependently-typed system. The proof is based on a translation of terms and types from P 2 T S into the λ-calculus. First, we deal with untyped terms, ensuring that reductions are faithfully mimicked in the λ-calculus. For this, we rely on an original encoding of the pattern matching capability of P 2 T S into the System Fω. Then we show how to translate types: the expressive power of System Fω is needed in order to fully reproduce the original typing judgments of P 2 T S . We prove that the encoding is correct with respect to reductions and typing, and we conclude with the strong normalization of simply-typed P 2 T S terms. The strong normalization with dependent types is in turn obtained by an intermediate translation into simply-typed terms

Principles of Superdeduction

International audienceIn predicate logic, the proof that a theorem P holds in a theory Th is typically conducted in natural deduction or in the sequent calculus using all the information contained in the theory in a uniform way. Introduced ten years ago, Deduction modulo allows us to make use of the computational part of the theory Th for true computations modulo which deductions are performed. Focussing on the sequent calculus, this paper presents and studies the dual concept where the theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. We call such a new deduction system "superdeduction''. We introduce a proof-term language and a cut-elimination procedure both based on Christian Urban's work on classical sequent calculus. Strong normalisation is proven under appropriate and natural hypothesis, therefore ensuring the consistency of the embedded theory and of the deduction system. The proofs obtained in such a new system are much closer to the human intuition and practice. We consequently show how superdeduction along with deduction modulo can be used to ground the formal foundations of new extendible proof assistants. We finally present lemuridae, our current implementation of superdeduction modulo

Efficacy of Half-Day Workshops for Internal Medicine Interns in Educating Breaking-Bad-News Discussions

Background: Adequate end-of-life (EOL) care/breaking-bad-news (BBN) discussions with patients are becoming increasingly essential to adequate patient care. Purpose: Whether a half-day workshop would lead to improved confidence in EOL/BBN care discussions for internal medicine interns. Methods: Internal medicine interns (n = 43) were assigned to participate in a half-day workshop at Thomas Jefferson University Hospital. The workshop involved two standardized patient (SP) interactions involving delivering news of a terminal illness/initiating goals of care discussion with the intervention of SP feedback, a didactic and lecture on proper EOL/BBN discussion. Voluntary anonymous surveys before and after the workshop were utilized to assess impact. Results: A majority of interns felt more comfortable with leading EOL care/BBN discussions after the workshop and had a positive experience. Conclusions: A half-day curriculum is efficacious in educating EOL/BBN communication to internal medicine interns, but should be further assessed in a larger more standardized study involving an objective assessment

The Role of Inhibition of Apoptosis in Acute Leukemias and Myelodysplastic Syndrome

Avoidance of apoptosis is a key mechanism that malignancies, including acute leukemias and MDS, utilize in order to proliferate and resist chemotherapy. Recently, venetoclax, an inhibitor of the anti-apoptotic protein BCL-2, has been approved for the treatment of upfront AML in an unfit, elderly population. This paper reviews the pre-clinical and clinical data for apoptosis inhibitors currently in development for the treatment of AML, ALL, and MDS