584 research outputs found
An inverse of the evaluation functional for typed Lambda-calculus
In any model of typed λ-calculus conianing some basic
arithmetic, a functional p - * (procedure—* expression)
will be defined which inverts the evaluation functional
for typed X-terms, Combined with the evaluation
functional, p-e yields an efficient normalization algorithm.
The method is extended to X-calculi with constants
and is used to normalize (the X-representations
of) natural deduction proofs of (higher order) arithmetic.
A consequence of theoretical interest is a strong
completeness theorem for βη-reduction, generalizing
results of Friedman [1] and Statman [31: If two Xterms
have the same value in some model containing
representations of the primitive recursive functions
(of level 1) then they are provably equal in the βη-
calculus
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
An inverse of the evaluation functional for typed Lambda-calculus
In any model of typed λ-calculus conianing some basic
arithmetic, a functional p - * (procedure—* expression)
will be defined which inverts the evaluation functional
for typed X-terms, Combined with the evaluation
functional, p-e yields an efficient normalization algorithm.
The method is extended to X-calculi with constants
and is used to normalize (the X-representations
of) natural deduction proofs of (higher order) arithmetic.
A consequence of theoretical interest is a strong
completeness theorem for βη-reduction, generalizing
results of Friedman [1] and Statman [31: If two Xterms
have the same value in some model containing
representations of the primitive recursive functions
(of level 1) then they are provably equal in the βη-
calculus
Control Lyapunov Functions and Stabilization by Means of Continuous Time-Varying Feedback
For a general time-varying system, we prove that existence of an "Output
Robust Control Lyapunov Function" implies existence of continuous time-varying
feedback stabilizer, which guarantees output asymptotic stability with respect
to the resulting closed-loop system. The main results of the present work
constitute generalizations of a well-known result towards feedback
stabilization due to J. M. Coron and L. Rosier concerning stabilization of
autonomous systems by means of time-varying periodic feedback.Comment: Submitted for possible publication to ESAIM Control, Optimisation and
Calculus of Variation
Paul Lorenzen -- Mathematician and Logician
This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science
Proof Systems for the Modal -Calculus Obtained by Determinizing Automata
Automata operating on infinite objects feature prominently in the theory of
the modal -calculus. One such application concerns the tableau games
introduced by Niwi\'{n}ski & Walukiewicz, of which the winning condition for
infinite plays can be naturally checked by a nondeterministic parity stream
automaton. Inspired by work of Jungteerapanich and Stirling we show how
determinization constructions of this automaton may be used to directly obtain
proof systems for the -calculus. More concretely, we introduce a binary
tree construction for determinizing nondeterministic parity stream automata.
Using this construction we define the annotated cyclic proof system
, where formulas are annotated by tuples of binary strings.
Soundness and Completeness of this system follow almost immediately from the
correctness of the determinization method
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.
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