Syntactic characterisations of amalgamation, convexity and related properties

1974 ◽  
Vol 39 (3) ◽  
pp. 433-451 ◽  
Author(s):  
Paul D. Bacsich ◽  
Dafydd Rowlands Hughes
Keyword(s):  
General Idea ◽  
Semantic Property ◽  
Cylindric Algebras ◽  
Real Numbers ◽  
Elementary Class ◽  
Preservation Theorems ◽  
Semantic Properties ◽  
Extra Structure

We prove that certain syntactic conditions similar to separation principles on a theory are equivalent to semantic properties such as amalgamation and strong amalgamation, by showing that appropriate classes of structures are definable by Lω1ω-sentences. Then we characterise the elements of core models and thus give a natural proof of Rabin's characterisation of convex theories.The notion of a syntactic characterisation of a semantic property of a theory is by now fairly well known. The earliest such were the classical preservation theorems: For example, a theorem of Lyndon characterised the theories whose models were closed under homomorphic images as those with a set of positive axioms.Presumably the notion of syntactic characterisation can be made precise, but it is probably better at this stage to leave it vague. The general idea is that theories are “algebras” (cylindric algebras, or logical categories, with suitable extra structure) and that a semantic property P of theories is syntactically characterisable if the class of theories with P is an “elementary” class of “algebras.”When one codes countable theories as real numbers, a syntactically characterisable property will be arithmetical. The converse does not seem reasonable, especially as it is often fairly easy to prove a property arithmetical (using extra predicates, usually), when we may not be able to find a syntactic characterisation.

scholarly journals Model theory of monadic predicate logic with the infinity quantifier

2021 ◽  
Author(s):  
Facundo Carreiro ◽  
Alessandro Facchini ◽  
Yde Venema ◽  
Fabio Zanasi
Keyword(s):  
Model Theory ◽  
Predicate Logic ◽  
Order Logic ◽  
First Order Logic ◽  
Semantic Property ◽  
First Order ◽  
Scott Continuous ◽  
Semantic Properties

AbstractThis paper establishes model-theoretic properties of $$\texttt {M} \texttt {E} ^{\infty }$$ M E ∞ , a variation of monadic first-order logic that features the generalised quantifier $$\exists ^\infty $$ ∃ ∞ (‘there are infinitely many’). We will also prove analogous versions of these results in the simpler setting of monadic first-order logic with and without equality ($$\texttt {M} \texttt {E} $$ M E and $$\texttt {M} $$ M , respectively). For each logic $$\texttt {L} \in \{ \texttt {M} , \texttt {M} \texttt {E} , \texttt {M} \texttt {E} ^{\infty }\}$$ L ∈ { M , M E , M E ∞ } we will show the following. We provide syntactically defined fragments of $$\texttt {L} $$ L characterising four different semantic properties of $$\texttt {L} $$ L -sentences: (1) being monotone and (2) (Scott) continuous in a given set of monadic predicates; (3) having truth preserved under taking submodels or (4) being truth invariant under taking quotients. In each case, we produce an effectively defined map that translates an arbitrary sentence $$\varphi $$ φ to a sentence $$\varphi ^\mathsf{p}$$ φ p belonging to the corresponding syntactic fragment, with the property that $$\varphi $$ φ is equivalent to $$\varphi ^\mathsf{p}$$ φ p precisely when it has the associated semantic property. As a corollary of our developments, we obtain that the four semantic properties above are decidable for $$\texttt {L} $$ L -sentences.

scholarly journals A practical primer on processing semantic property norm data

2019 ◽  
Author(s):  
Erin Michelle Buchanan ◽  
Simon De Deyne ◽  
Maria Montefinese
Keyword(s):  
Lexical Processing ◽  
Semantic Property ◽  
Test Context ◽  
Processing Pipeline ◽  
Specific Concept ◽  
Methodological Aspects ◽  
The Impact ◽  
Semantic Properties

Semantic property listing tasks require participants to generate short propositions (e.g., \<*barks*\>, \<*has fur*\>) for a specific concept (e.g., dog). This task is the cornerstone of the creation of semantic property norms which are essential for modelling, stimuli creation, and understanding similarity between concepts. However, despite the wide applicability of semantic property norms for a large variety of concepts across different groups of people, the methodological aspects of the property listing task have received less attention, even though the procedure and processing of the data can substantially affect the nature and quality of the measures derived from them. The goal of this paper is to provide a practical primer on how to collect and process semantic property norms. We will discuss the key methods to elicit semantic properties and compare different methods to derive meaningful representations from them. This will cover the role of instructions and test context, property pre-processing (e.g., lemmatization), property weighting, and relationship encoding using ontologies. With these choices in mind, we propose and demonstrate a processing pipeline that transparently documents these steps resulting in improved comparability across different studies. The impact of these choices will be demonstrated using intrinsic (e.g., reliability, number of properties) and extrinsic measures (e.g., categorization, semantic similarity, lexical processing). This practical primer will offer potential solutions to several longstanding problems and allow researchers to develop new property listing norms overcoming the constraints of previous studies.

The expressive function of language

2019 ◽  
pp. 10-34
Author(s):  
Daniel Gutzmann
Keyword(s):  
Historical Perspective ◽  
Semantic Analysis ◽  
Expressive Language ◽  
General Idea ◽  
Specific System ◽  
Semantic Approach ◽  
Expressive Function ◽  
Expressive Meaning ◽  
Main Ideas ◽  
Semantic Properties

This chapter offers a very brief historical perspective on the notion of expressivity and introduces the general idea of hybrid semantics, before presenting various instances of expressions fulfilling the expressive language function, and the tools for their semantic analysis. The three main phenomena of this book will be introduced (expressive adjectives, expressive intensifiers, and expressive vocatives) and the specific semantic properties of expressive meaning will be discussed. The second half of the chapter provides an overview of recent formal approaches to expressivity and sketches the main ideas of a formal semantic approach to expressive meaning that is based on the idea of a multidimensional system, before presenting the specific system that will be used for the purposes of the case studies in this book.

scholarly journals Bare Root Infinitives in German

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Irene Rapp ◽  
Susanne Riecker ◽  
Saskia Brockmann ◽  
Christian Fortmann ◽  
Jonas Bozenhard
Keyword(s):  
Semantic Analysis ◽  
Linguistic Analysis ◽  
Semantic Property ◽  
Joint Work ◽  
Everyday Language ◽  
Text Interpretation ◽  
Bare Root ◽  
Linguistic Structures ◽  
Semantic Properties

The aim of this paper is to show how linguistic and literary studies can benefit from a joint work about linguistic structures in poetry. Firstly, the analysis of poetry has an important impact on linguistic theory as it leads our attention to specific structures and meanings that so far have not been considered. Secondly, a close linguistic analysis can reveal hitherto overlooked facets of meaning which have a great significance for the overall interpretation of a poem. We focus on Bare Root Infinitives (BRIs) in German. As they lack the features for tense, mood, person and number, they are more flexible in meaning than finite forms. When looking at poetry, besides the well-known deontic and bouleticmeanings (cf. Reis 1995, 2003; Gärtner 2014) a third meaning that we call reactive meaning stands out. Remarkably, this reactive meaning can also be found in everyday language. Its specific semantic properties show that a semantic analysis of BRIs in the style of Kaufmann (2012) is adequate: modality, but not non-referentiality, is a “hard-wired” semantic property of BRIs. The specific case study of the poem ‘muster fixieren’ (‘fixating patterns’) by Nico Bleutge reveals how the restricted context of the poem interacts with the different interpretations of BRIs to arrive at a complex text interpretation. Keywords: bare root infinitives, semantic-pragmatic interface, poetry, modality, pragmatic enrichment, semantics

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

What Does Human Development Index Rating Mean in Terms of Individualism/Collectivism?

2003 ◽  
Vol 8 (2) ◽  
pp. 97-100 ◽  
Author(s):  
Maria José Sotelo ◽  
Luis Gimeno
Keyword(s):  
Human Development ◽  
Human Development Index ◽  
Principal Component ◽  
General Idea ◽  
Development Index ◽  
Low Levels ◽  
The Relationship

The authors explore an alternative way of analyzing the relationship between human development and individualism. The method is based on the first principal component of Hofstede's individualism index in the Human Development Index rating domain. Results suggest that the general idea that greater wealth brings more individualism is only true for countries with high levels of development, while for middle or low levels of development the inverse is true.

Semantic Properties Questionnaire

2002 ◽  
Author(s):  
Stanley B. Klein ◽  
Leda Cosmides ◽  
Kristi A. Costabile ◽  
Lisa Mei
Keyword(s):  
Semantic Properties
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