scholarly journals Formal metatheory of second-order abstract syntax

2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-29
Author(s):  
Marcelo Fiore ◽  
Dmitrij Szamozvancev

Despite extensive research both on the theoretical and practical fronts, formalising, reasoning about, and implementing languages with variable binding is still a daunting endeavour – repetitive boilerplate and the overly complicated metatheory of capture-avoiding substitution often get in the way of progressing on to the actually interesting properties of a language. Existing developments offer some relief, however at the expense of inconvenient and error-prone term encodings and lack of formal foundations. We present a mathematically-inspired language-formalisation framework implemented in Agda. The system translates the description of a syntax signature with variable-binding operators into an intrinsically-encoded, inductive data type equipped with syntactic operations such as weakening and substitution, along with their correctness properties. The generated metatheory further incorporates metavariables and their associated operation of metasubstitution, which enables second-order equational/rewriting reasoning. The underlying mathematical foundation of the framework – initial algebra semantics – derives compositional interpretations of languages into their models satisfying the semantic substitution lemma by construction.

2020 ◽  
Author(s):  
Jan Aldert Bergstra ◽  
John V. Tucker

In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and -1/0 equal to its opposite, and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics.


2004 ◽  
Vol 13 (03n04) ◽  
pp. 423-426 ◽  
Author(s):  
L. SANGUINET ◽  
S. AHMED ◽  
J. L. POZZO ◽  
V. RODRIGUEZ ◽  
F. ADAMIETZ

New acidochromic and photochromic compounds with nonlinear optical properties have been designed and synthesized. The hyperpolarizabilities of the zwitterionic colored forms have been quantified with polarized hyper-Rayleigh scattering experiments. The static value of oxazolidino-indoline 2 is found to be as high as Disperse Red One. This opens the way to novel multi-addressable NLO-systems.


1977 ◽  
Vol 24 (1) ◽  
pp. 68-95 ◽  
Author(s):  
J. A. Goguen ◽  
J. W. Thatcher ◽  
E. G. Wagner ◽  
J. B. Wright

2021 ◽  
Vol vol. 23 no. 1 (Automata, Logic and Semantics) ◽  
Author(s):  
Zoltán Fülöp ◽  
Dávid Kószó ◽  
Heiko Vogler

We consider weighted tree automata (wta) over strong bimonoids and their initial algebra semantics and their run semantics. There are wta for which these semantics are different; however, for bottom-up deterministic wta and for wta over semirings, the difference vanishes. A wta is crisp-deterministic if it is bottom-up deterministic and each transition is weighted by one of the unit elements of the strong bimonoid. We prove that the class of weighted tree languages recognized by crisp-deterministic wta is the same as the class of recognizable step mappings. Moreover, we investigate the following two crisp-determinization problems: for a given wta ${\cal A}$, (a) does there exist a crisp-deterministic wta which computes the initial algebra semantics of ${\cal A}$ and (b) does there exist a crisp-deterministic wta which computes the run semantics of ${\cal A}$? We show that the finiteness of the Nerode algebra ${\cal N}({\cal A})$ of ${\cal A}$ implies a positive answer for (a), and that the finite order property of ${\cal A}$ implies a positive answer for (b). We show a sufficient condition which guarantees the finiteness of ${\cal N}({\cal A})$ and a sufficient condition which guarantees the finite order property of ${\cal A}$. Also, we provide an algorithm for the construction of the crisp-deterministic wta according to (a) if ${\cal N}({\cal A})$ is finite, and similarly for (b) if ${\cal A}$ has finite order property. We prove that it is undecidable whether an arbitrary wta ${\cal A}$ is crisp-determinizable. We also prove that both, the finiteness of ${\cal N}({\cal A})$ and the finite order property of ${\cal A}$ are undecidable.


Gesture ◽  
2011 ◽  
Vol 11 (3) ◽  
pp. 241-270 ◽  
Author(s):  
Michael Lempert

Gesture in political oratory and debate is renowned for its nonreferential indexical functions, for the way it purportedly can indicate qualities of speaker and materialize acts of persuasion — functions famously addressed in Quintilian’s classic writings but understudied today. I revisit this problematic through a case study of precision-grip (especially thumb to tip of forefinger) in Barack Obama’s debate performances (2004–2008). Cospeech gesture can index valorized attributes of speaker — not directly but through orders of semiotic motivation. In terms of first-order indexicality, precision-grip highlights discourse in respect of information structure, indicating focus. In debate, precision grip has undergone a degree of conventionalization and has reemerged as a second-order pragmatic resource for performatively “making a ‘sharp’, effective point.” Repetitions and parallelisms of precision grip in debate can, in turn, exhibit speaker-attributes, such as being argumentatively ‘sharp’, and from there may even partake in candidate branding.


2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Jaco Gericke

In this article, a supplementary yet original contribution is made to the ongoing attempts at refining ways of comparative-philosophical conceptual clarification of Qohelet’s claim that הבל הכל in 1:2 (and 12:8). Adopting and adapting the latest analytic metaphysical concerns and categories for descriptive purposes only, a distinction is made between הבל as property of הכל and the properties of הבל in relation to הכל. Involving both correlation and contrast, the second-order language framework is hereby extended to a level of advanced nuance and specificity for restating the meaning of the book’s first-order language on its own terms, even if not in them.Contribution: By considering logical, ontological, mereological and typological aspects of property theory in dialogue with appearances of הכל and of הבל in Ecclesiastes 1:2 and 12:8 and in-between, a new way is presented in the quest to explain why things in the world of the text are the way they are, or why they are at all.


Author(s):  
C.A.J. Coady

Philosophical treatment of the problems posed by the concept of knowledge has been curiously blind to the role played by testimony in the accumulation and validation of knowledge or, for that matter, justified belief. This is all the more surprising, given that an enormous amount of what any individual can plausibly claim to know, whether in everyday affairs or in theoretical pursuits, is dependent in various ways upon what others have to say. The idea that someone can only really attain knowledge if they get it entirely by the use of their own resources provides a seductive ideal of autonomous knowledge that may help explain the way epistemologists have averted their gaze from the topic of testimony. But, unless they are prepared to limit the scope of knowledge dramatically, theorists who support this individualist ideal of autonomy need to explain how our wide-ranging reliance upon what we are told is consistent with it. Characteristically, those who consider the matter acknowledge the reliance, but seek to show that the individual cognizer can ‘justify’ dependence upon testimony by sole resort to the individual’s resources of observation, memory and inference. Testimony is thus viewed as a second-order source of knowledge. But this reductionist project is subject to major difficulties, as can be seen in David Hume’s version. It has problems with the way the proposed justification is structured, with its assumptions about language and with the way the individual’s epistemic resources are already enmeshed with testimony. The success or failure of the reductionist project has significant implications for other areas of inquiry.


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