scholarly journals Star-Freeness, First-Order Definability and Aperiodicity of Structured Context-Free Languages

2020 ◽  
pp. 161-180
Author(s):  
Dino Mandrioli ◽  
Matteo Pradella ◽  
Stefano Crespi Reghizzi
Keyword(s):  
First Order ◽  
Context Free ◽  
First Order Definability

Simulating polyadic modal logics by monadic ones

2003 ◽  
Vol 68 (2) ◽  
pp. 419-462 ◽  
Author(s):  
George Goguadze ◽  
Carla Piazza ◽  
Yde Venema
Keyword(s):  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
First Order ◽  
First Order Definability

AbstractWe define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic Λsim in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/recursive axiomatizability, frame completeness and the finite model property, canonicity and first-order definability.

An undecidable problem in correspondence theory

1991 ◽  
Vol 56 (4) ◽  
pp. 1261-1272 ◽  
Author(s):  
L. A. Chagrova
Keyword(s):  
Correspondence Theory ◽  
First Order ◽  
Undecidable Problem ◽  
First Order Definability ◽  
Effective Procedures

In this paper we prove undecidability of first-order definability of propositional formulas. The main result is proved for intuitionistic formulas, but it remains valid for other kinds of propositional formulas by analogous arguments or with the help of various translations.For general background on correspondence theory the reader is referred to van Benthem [1], [2] (see [3] for a survey of recent results).The method for the proofs of undecidability in this paper will be to simulate calculations of a Minsky machine by intuitionistic formulas. §3 concerns this simulation. Effective procedures for the construction of simulating modal formulas can be found in the literature (cf. [4]).The principal results of the paper are in §4. §5 gives some further undecidability results, that will be proved in another paper by modification of the method of this paper.I am indebted to the referee for drawing my attention to some errors in an earlier version of this paper.

scholarly journals Functional first order definability of LRTP

2010 ◽  
Vol 14 (48) ◽  
Author(s):  
José Raymundo Marcial Romero ◽  
José Antonio Hernández
Keyword(s):  
First Order ◽  
First Order Definability

First-order definability

2004 ◽  
pp. 151-174
Author(s):  
Richard Lassaigne ◽  
Michel de Rougemont
Keyword(s):  
First Order ◽  
First Order Definability

First-order definability in modal logic

1975 ◽  
Vol 40 (1) ◽  
pp. 35-40 ◽  
Author(s):  
R. I. Goldblatt
Keyword(s):  
Modal Logic ◽  
Binary Relation ◽  
Second Order ◽  
Order Conditions ◽  
Kripke Models ◽  
Order Condition ◽  
First Order ◽  
Axiom Systems ◽  
Set Of Points ◽  
First Order Definability

In the early days of the development of Kripke-style semantics for modal logic a great deal of effort was devoted to showing that particular axiom systems were characterised by a class of models describable by a first-order condition on a binary relation. For a time the approach seemed all encompassing, but recent work by Thomason [6] and Fine [2] has shown it to be somewhat limited—there are logics not determined by any class of Kripke models at all. In fact it now seems that modal logic is basically second-order in nature, in that any system may be analysed in terms of structures having a nominated class of second-order individuals (subsets) that serve as interpretations of propositional variables (cf. [7]). The question has thus arisen as to how much of modal logic can be handled in a first-order way, and precisely which modal sentences are determined by first-order conditions on their models. In this paper we present a model-theoretic characterisation of this class of sentences, and show that it does not include the much discussed LMp → MLp.Definition 1. A modal frame ℱ = 〈W, R〉 consists of a set W on which a binary relation R is defined. A valuation V on ℱ is a function that associates with each propositional variable p a subset V(p) of W (the set of points at which p is “true”).

scholarly journals ALGEBRAIC LINEAR ORDERINGS

2011 ◽  
Vol 22 (02) ◽  
pp. 491-515 ◽  
Author(s):  
S. L. BLOOM ◽  
Z. ÉSIK
Keyword(s):  
Order Type ◽  
Linear Ordering ◽  
Type Result ◽  
First Order ◽  
Linear Orderings ◽  
Context Free Language ◽  
Categorical Algebra ◽  
Context Free ◽  
Free Language

An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general Mezei-Wright type result, algebraic linear orderings are exactly those isomorphic to the linear ordering of the leaves of an algebraic tree. Using Courcelle's characterization of algebraic trees, we obtain the fact that a linear ordering is algebraic if and only if it can be represented as the lexicographic ordering of a deterministic context-free language. When the algebraic linear ordering is a well-ordering, its order type is an algebraic ordinal. We prove that the Hausdorff rank of any scattered algebraic linear ordering is less than ωω. It follows that the algebraic ordinals are exactly those less than ωωω.

Sign in / Sign up

Export Citation Format

Share Document