Wyniki wyszukiwania

1

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus

100%

Indrzejczak A.

Bulletin of the Section of Logic

|

2016

|

tom 45

|

nr 2

EN

In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi (SC) for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but with some additional simple rewrite rules. The procedure combines the proces of saturation of sequents with reduction of their elements to some normal modal form.

2

A Post-style proof of completeness theorem for symmetric relatedness Logic S

100%

Klonowski M.

Bulletin of the Section of Logic

|

2018

|

tom 47

|

nr 3

EN

One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2] we can find some open problems concerning relatedness logic, a Post-style completeness theorem for logic S is one of them. Our paper introduces a solution of this metalogical issue.

3

Diffusion times and stability exponents for nearly integrable analytic systems

75%

Lochak P., Marco J.-P.

Open Mathematics

|

2005

|

tom 3

|

nr 3

342-397

EN

For a positive integer n and R>0, we set $$B_R^n = \left\{ {x \in \mathbb{R}^n |\left\| x \right\|_\infty< R} \right\}$$ . Given R>1 and n≥4 we construct a sequence of analytic perturbations (H j) of the completely integrable Hamiltonian $$h\left( r \right) = \tfrac{1}{2}r_1^2 + ...\tfrac{1}{2}r_{n - 1}^2 + r_n $$ on $$\mathbb{T}^n \times B_R^n $$ , with unstable orbits for which we can estimate the time of drift in the action space. These functions H j are analytic on a fixed complex neighborhood V of $$\mathbb{T}^n \times B_R^n $$ , and setting $$\varepsilon _j : = \left\| {h - H_j } \right\|_{C^0 (V)} $$ the time of drift of these orbits is smaller than (C(1/ɛ j)1/2(n-3)) for a fixed constant c>0. Our unstable orbits stay close to a doubly resonant surface, the result is therefore almost optimal since the stability exponent for such orbits is 1/2(n−2). An analogous result for Hamiltonian diffeomorphisms is also proved. Two main ingredients are used in order to deal with the analytic setting: a version of Sternberg's conjugacy theorem in a neighborhood of a normally hyperbolic manifold in a symplectic system, for which we give a complete (and seemingly new) proof; and Easton windowing method that allow us to approximately localize the wandering orbits and estimate their speed of drift.

Ograniczanie wyników

2 Bulletin of the Section of Logic

1 Open Mathematics

1 Indrzejczak A.

1 Klonowski M.

1 Lochak P.

1 Marco J.-P.

1 2018

1 2016

1 2005

Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus

A Post-style proof of completeness theorem for symmetric relatedness Logic S

Diffusion times and stability exponents for nearly integrable analytic systems