On the Expressive Power of GF(2)-Grammars

2019 ◽  
pp. 310-323 ◽  
Author(s):  
Vladislav Makarov ◽  
Alexander Okhotin
Keyword(s):  
Expressive Power

Recursive generation in language

2017 ◽  
Author(s):  
David J. Lobina
Keyword(s):  
Mathematical Logic ◽  
Production System ◽  
General Property ◽  
Recent Literature ◽  
Expressive Power ◽  
The Self ◽  
Recursive Structure ◽  
Embedded Structures ◽  
Mechanical Procedure ◽  
The 1950S

The introduction of recursion into linguistics was the result of applying some of the results of mathematical logic to the study of language. In particular, recursion was introduced in the 1950s as a general property of the mechanical procedure underlying the grammar, in order to account for language’s discrete infinity and expressive power—in the 1950s, this mechanical procedure was a production system, whereas more recently, of course, it is the set-operator merge. Unfortunately, the recent literature has confused the general recursive property of a grammar with specific instances of (recursive) rules/operations within a grammar; more worryingly still, there has been a general conflation of these recursive rules with some of the self-embedded structures these rules can generate, adding to the confusion. The conflation is manifold but always fallacious. Moreover, language manifests a much more generally recursive structure than is usually recognized: bundles of the universal (Specifier)-Head-Complement(s) geometry.

scholarly journals Probability logic: A model-theoretic perspective

2020 ◽  
Author(s):  
M Pourmahdian ◽  
R Zoghifard
Keyword(s):  
Characterization Theorem ◽  
Expressive Power ◽  
Probability Logic ◽  
Theoretic Analysis ◽  
Compactness Property ◽  
Probability Models ◽  
Finitely Additive Probability ◽  
Additive Probability ◽  
Basic Probability ◽  
Abstract Logics

Abstract This paper provides some model-theoretic analysis for probability (modal) logic ($PL$). It is known that this logic does not enjoy the compactness property. However, by passing into the sublogic of $PL$, namely basic probability logic ($BPL$), it is shown that this logic satisfies the compactness property. Furthermore, by drawing some special attention to some essential model-theoretic properties of $PL$, a version of Lindström characterization theorem is investigated. In fact, it is verified that probability logic has the maximal expressive power among those abstract logics extending $PL$ and satisfying both the filtration and disjoint unions properties. Finally, by alternating the semantics to the finitely additive probability models ($\mathcal{F}\mathcal{P}\mathcal{M}$) and introducing positive sublogic of $PL$ including $BPL$, it is proved that this sublogic possesses the compactness property with respect to $\mathcal{F}\mathcal{P}\mathcal{M}$.

The Complexity of Model-Checking Tail-Recursive Higher-Order Fixpoint Logic

2021 ◽  
Vol 178 (1-2) ◽  
pp. 1-30
Author(s):  
Florian Bruse ◽  
Martin Lange ◽  
Etienne Lozes
Keyword(s):  
Model Checking ◽  
Lower Bounds ◽  
Expressive Power ◽  
Higher Order ◽  
Order Logic ◽  
High Complexity ◽  
Transition Systems ◽  
Recursive Formulas ◽  
Second Order Logic ◽  
Monadic Second Order Logic

Higher-Order Fixpoint Logic (HFL) is a modal specification language whose expressive power reaches far beyond that of Monadic Second-Order Logic, achieved through an incorporation of a typed λ-calculus into the modal μ-calculus. Its model checking problem on finite transition systems is decidable, albeit of high complexity, namely k-EXPTIME-complete for formulas that use functions of type order at most k < 0. In this paper we present a fragment with a presumably easier model checking problem. We show that so-called tail-recursive formulas of type order k can be model checked in (k − 1)-EXPSPACE, and also give matching lower bounds. This yields generic results for the complexity of bisimulation-invariant non-regular properties, as these can typically be defined in HFL.

scholarly journals Audio-to-score singing transcription based on a CRNN-HSMM hybrid model

2021 ◽  
Vol 10 ◽  
Author(s):  
Ryo Nishikimi ◽  
Eita Nakamura ◽  
Masataka Goto ◽  
Kazuyoshi Yoshii
Keyword(s):  
Hybrid Model ◽  
Viterbi Algorithm ◽  
Language Model ◽  
Expressive Power ◽  
Acoustic Model ◽  
Musical Language ◽  
Musical Score ◽  
Singing Voice ◽  
Generative Process ◽  
Music Signal

This paper describes an automatic singing transcription (AST) method that estimates a human-readable musical score of a sung melody from an input music signal. Because of the considerable pitch and temporal variation of a singing voice, a naive cascading approach that estimates an F0 contour and quantizes it with estimated tatum times cannot avoid many pitch and rhythm errors. To solve this problem, we formulate a unified generative model of a music signal that consists of a semi-Markov language model representing the generative process of latent musical notes conditioned on musical keys and an acoustic model based on a convolutional recurrent neural network (CRNN) representing the generative process of an observed music signal from the notes. The resulting CRNN-HSMM hybrid model enables us to estimate the most-likely musical notes from a music signal with the Viterbi algorithm, while leveraging both the grammatical knowledge about musical notes and the expressive power of the CRNN. The experimental results showed that the proposed method outperformed the conventional state-of-the-art method and the integration of the musical language model with the acoustic model has a positive effect on the AST performance.

scholarly journals Categorification of the Müller-Wichards System Performance Estimation Model: Model Symmetries, Invariants, and Closed Forms

Systems ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 6
Author(s):  
Allen D. Parks ◽  
David J. Marchette
Keyword(s):  
Closed Form ◽  
System Performance ◽  
Algebraic Method ◽  
Expressive Power ◽  
Computer Applications ◽  
Performance Estimation ◽  
Parallel Computer ◽  
Estimation Model ◽  
Data Movement ◽  
Fundamental Symmetry

The Müller-Wichards model (MW) is an algebraic method that quantitatively estimates the performance of sequential and/or parallel computer applications. Because of category theory’s expressive power and mathematical precision, a category theoretic reformulation of MW, i.e., CMW, is presented in this paper. The CMW is effectively numerically equivalent to MW and can be used to estimate the performance of any system that can be represented as numerical sequences of arithmetic, data movement, and delay processes. The CMW fundamental symmetry group is introduced and CMW’s category theoretic formalism is used to facilitate the identification of associated model invariants. The formalism also yields a natural approach to dividing systems into subsystems in a manner that preserves performance. Closed form models are developed and studied statistically, and special case closed form models are used to abstractly quantify the effect of parallelization upon processing time vs. loading, as well as to establish a system performance stationary action principle.

scholarly journals INFINITARY PROPOSITIONAL RELEVANT LANGUAGES WITH ABSURDITY

2017 ◽  
Vol 10 (4) ◽  
pp. 663-681
Author(s):  
GUILLERMO BADIA
Keyword(s):  
Expressive Power ◽  
Interpolation Theorem ◽  
Boolean Logic ◽  
Isomorphism Theorem ◽  
Strong Completeness ◽  
Lack Of Compactness ◽  
Relevant Logics ◽  
Beth Definability ◽  
Beth Definability Property

AbstractAnalogues of Scott’s isomorphism theorem, Karp’s theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant logics. An “interpolation theorem” (of a particular sort introduced by Barwise and van Benthem) for the infinitary quantificational boolean logic L∞ω holds. This yields a preservation result characterizing the expressive power of infinitary relevant languages with absurdity using the model-theoretic relation of relevant directed bisimulation as well as a Beth definability property.

scholarly journals Constructing weak simulations from linear implications for processes with private names

2019 ◽  
Vol 29 (8) ◽  
pp. 1275-1308 ◽  
Author(s):  
Ross Horne ◽  
Alwen Tiu
Keyword(s):  
Expressive Power ◽  
Dual Pair ◽  
Proof System ◽  
Branching Time ◽  
First Order ◽  
Order Extension

AbstractThis paper clarifies that linear implication defines a branching-time preorder, preserved in all contexts, when used to compare embeddings of process in non-commutative logic. The logic considered is a first-order extension of the proof system BV featuring a de Morgan dual pair of nominal quantifiers, called BV1. An embedding of π-calculus processes as formulae in BV1 is defined, and the soundness of linear implication in BV1 with respect to a notion of weak simulation in the π -calculus is established. A novel contribution of this work is that we generalise the notion of a ‘left proof’ to a class of formulae sufficiently large to compare embeddings of processes, from which simulating execution steps are extracted. We illustrate the expressive power of BV1 by demonstrating that results extend to the internal π -calculus, where privacy of inputs is guaranteed. We also remark that linear implication is strictly finer than any interleaving preorder.

scholarly journals The expressive power of indeterminate dataflow primitives

1992 ◽  
Vol 98 (1) ◽  
pp. 99-131 ◽  
Author(s):  
Prakash Panangaden ◽  
Vasant Shanbhogue
Keyword(s):  
Expressive Power
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