Intensional logic and two-sorted type theory

1989 ◽  
Vol 54 (1) ◽  
pp. 65-77 ◽  
Author(s):  
Thomas Ede Zimmermann
Keyword(s):  
Natural Language ◽  
Type Theory ◽  
Formal Languages ◽  
Expressive Power ◽  
Basic Type ◽  
The Other ◽  
Intensional Logic ◽  
Exact Relation ◽  
Standard Validity ◽  
Translation Procedure

Among the symbolic languages used most frequently in the indirect interpretation of natural language are Montague's Intensional Logic IL [5, 384ff.] and its extensional counterpart, the language Ty2 of two-sorted type theory. The question of which of these two formal languages is to be preferred has been obscured by lack of knowledge about the exact relation between them. The present paper is an attempt to clarify the situation by showing that, modulo a small, decidable class of formulas irrelevant to these applications, IL and Ty2 are equivalent in the strong sense that there exists a reversible translation between the terms of either language.In [3, 6Iff.] Gallin has shown that there exists a simple and natural translation * of IL into Ty2. Following Gallin's translation procedure, it is even possible to conceive of IL as a highly restricted sublanguage of Ty2, viz. as that part which only contains expressions of certain intensional types plus one variable of the basic type of indices or worlds. In an obvious sense, this sublanguage has less expressive power than the whole of Ty2, where it is possible to express conditions on entities that do not even exist in IL's ontology. However, by a certain amount of coding, one can translate Ty2 into IL [3, 105]. Conditions on nonintensional entities then become conditions on corresponding intensional objects; and these paraphrases preserve (standard) validity and entailment. On the other hand, this retranslation of Ty2 into IL is not an inversion of *, as can be seen from a simple example.

scholarly journals Copyful Streaming String Transducers

2021 ◽  
Vol 178 (1-2) ◽  
pp. 59-76
Author(s):  
Emmanuel Filiot ◽  
Pierre-Alain Reynier
Keyword(s):  
Polynomial Time ◽  
Equivalence Problem ◽  
Expressive Power ◽  
The Other ◽  
Finite State Automata ◽  
Finite State ◽  
Variable Content ◽  
Deterministic Automata ◽  
Intermediate Output ◽  
Linear Manner

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Černý in 2010 as a one-way deterministic automata model to define transductions of finite strings. Copyless SST extend deterministic finite state automata with a set of variables in which to store intermediate output strings, and those variables can be combined and updated all along the run, in a linear manner, i.e., no variable content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string transductions, and are as expressive as deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decidable equivalence problem (in PSpace). On the other hand, HDT0L systems have been introduced for a while, the most prominent result being the decidability of the equivalence problem. In this paper, we propose a semantics of HDT0L systems in terms of transductions, and use it to study the class of deterministic copyful SST. Our contributions are as follows: (i)HDT0L systems and total deterministic copyful SST have the same expressive power, (ii)the equivalence problem for deterministic copyful SST and the equivalence problem for HDT0L systems are inter-reducible, in quadratic time. As a consequence, equivalence of deterministic SST is decidable, (iii)the functionality of non-deterministic copyful SST is decidable, (iv)determining whether a non-deterministic copyful SST can be transformed into an equivalent non-deterministic copyless SST is decidable in polynomial time.

Tense

2009 ◽  
Author(s):  
Peter Ludlow
Keyword(s):  
Natural Language ◽  
The Other ◽  
Good Case ◽  
Other Hand ◽  
Insight Into

While most approaches to the semantics of tense have attempted to regiment tense away in a tenseless metalanguage, a good case can be made that this is not without cost (the same case could be made for regimentation of modality and other aspects of natural language as well). On the other hand, it is pretty clear that attempts to treat tense in a tensed metalanguage introduce serious complications. It is probably not so important which of these positions is correct at this point (we may be some distance from resolving that question), as it is that we understand the costs of the respective positions. Perhaps, by having a firm enough grasp on both approaches we afford ourselves a deeper insight into the nature of tense itself.

Models and Reality

2019 ◽  
pp. 128-153
Author(s):  
Stephen Yablo
Keyword(s):  
Model Theory ◽  
Expressive Power ◽  
The Other ◽  
Hilary Putnam ◽  
Objective World ◽  
Other Hand ◽  
Cast Doubt

The philosopher Hilary Putnam uses model theory to cast doubt on our ability to engage semantically with an objective world. The role of mathematics for him is to prove this pessimistic conclusion. The present chapter, on the other hand, explores how models can help us to engage semantically with the objective world. Mathematics functions here as an analogy. Among their many other accomplishments, numbers boost the language’s expressive power; they give us access to recondite physical facts. Models, among their many other accomplishments, do the same thing. This is the analogy this chapter attempts to develop.

Natural Shell

2016 ◽  
Vol 5 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Xiao Liu ◽  
Yufei Jiang ◽  
Lawrence Wu ◽  
Dinghao Wu
Keyword(s):  
Natural Language ◽  
End Users ◽  
The Other ◽  
Prototype System ◽  
Online Forums ◽  
Skill Levels ◽  
Scripting Languages ◽  
Other Hand

Scripting is a widely-used way to automate the execution of tasks. Despite the popularity of scripting, it remains difficult to use for both beginners and experts: because of the cryptic commands for the first group, and incompatible syntaxes across different systems, for the latter group. The authors introduce Natural Shell, an assistant for enabling end-users to generate commands and scripts for various purposes. Natural Shell automatically synthesizes scripts for different shell systems based on natural language descriptions. By interacting with Natural Shell, new users can learn the basics of scripting languages without the obstacles from the incomprehensible syntaxes. On the other hand, the authors' tool frees more advanced users from manuals when they switch shell systems. The authors have developed a prototype system and demonstrate its effectiveness with a benchmark of 50 examples of popular shell commands collected from online forums. In addition, the authors analyzed the usage of Natural Shell in a lab study that involves 10 participants with different scripting skill levels. Natural Shell effectively assists the users to generate commands in assigned syntaxes and greatly streamlines their learning and using experience.

Constructing the Impossible

2021 ◽  
pp. 141-163
Author(s):  
Kit Fine
Keyword(s):  
Natural Language ◽  
Possible Worlds ◽  
Formal Languages ◽  
Impossible Worlds ◽  
Possible World ◽  
Limited Role ◽  
Wide Range ◽  
Degree Of Acceptance ◽  
Broad Role ◽  
Natural Way

Please keep the original abstract. A number of philosophers have flirted with the idea of impossible worlds and some have even become enamored of it. But it has not met with the same degree of acceptance as the more familiar idea of a possible world. Whereas possible worlds have played a broad role in specifying the semantics for natural language and for a wide range of formal languages, impossible worlds have had a much more limited role; and there has not even been general agreement as to how a reasonable theory of impossible worlds is to be developed or applied. This chapter provides a natural way of introducing impossible states into the framework of truthmaker semantics and shows how their introduction permits a number of useful applications.

A simple traffic-light semiotic model for tagmemic theory

Semiotica ◽  
2018 ◽  
Vol 2018 (225) ◽  
pp. 253-267
Author(s):  
Vern Poythress
Keyword(s):  
Natural Language ◽  
The Other ◽  
Multiple Views ◽  
Semiotic Analysis ◽  
Traffic Light ◽  
Semiotic System ◽  
Traffic Lights ◽  
Semiotic Model ◽  
Semiotic Approach ◽  
Field View

AbstractThe complexity and flexibility of tagmemic theory, as a semiotic theory developed by Kenneth L. Pike, can be better understood by examining how it applies to a simple semiotic system like traffic lights. We can then compare the result with how it functions in analyzing a piece of natural language. Tagmemic theory introduces three observer viewpoints – the particle view, the wave view, and the field view. Each view generates a suite of questions to answer. Any one of the views results in a “complete” description of traffic lights, from which the information about the other views can be inferred. And yet each view is distinct in texture from the others, and the existence of such multiple views – each with a claim to emic integrity and each serving as a perspective on the whole – has to be accounted for in a robust semiotic approach. The same phenomena occur when we apply the three views to the analysis of meaning in natural language. The chief illustration is to analyze the meaning of the word dog in multiple ways. The multi-dimensional potential for semiotic analysis highlights the limitations of Aristotelian logic and symbolic logic, both of which simplify for the sake of rigor.

scholarly journals The Development, Morphology and Budding of the Ascidian Diazona

1948 ◽  
Vol 27 (2) ◽  
pp. 389-399 ◽  
Author(s):  
N. J. Berrill
Keyword(s):  
Life Cycle ◽  
Asexual Reproduction ◽  
Basic Type ◽  
The Other ◽  
Strong Argument ◽  
Bud Formation ◽  
Present Account ◽  
The Family ◽  
The One ◽  
Complete Account

Diazona is represented in European waters only by Diazona violacea Savigny. It is a compound ascidian forming massive colonies of spectacular size and appearance. In many ways it is the most interesting of all ascidians, for in its adult structure it straddles two commonly accepted orders and in itself is a strong argument against such a division; it is the only oviparous and small egged compound ascidian, two features undoubtedly primitive; and its manner of budding is the simplest and probably is the basic type for the group as a whole. Only fragmentary descriptions of the morphology and reproduction exist, and a more or less complete account of the various stages of the life cycle may be of some value. The family Diazonidae includes, in addition to Diazona itself, the genera Tylobranchion of subantarctic regions, and Rhopalea of Mediterranean and northern waters. In its entirety Diazona appears to link with such divergent forms as Ciona on the one hand and Archidistoma on the other. The fact that Diazona is obtained by dredging in relatively swift offshore waters and lives poorly in an aquarium probably accounts for the existing unsatisfactory state of knowledge of most of its phases. Most of what is known concerns asexual reproduction; and attention has been given, at various times, primarily to the process of regeneration, rather than bud formation, for example by Della Valle (1884), Caullery (1914), Oka (1906) under the name Aphanobranchion, and by Salfi (1926).The material of the present account was collected at various times in the Plymouth area from the Mewstone and Eddystone grounds.

Lambda Calculus, Type Theory, and Natural Language II

2007 ◽  
Vol 18 (2) ◽  
pp. 203-203
Author(s):  
C. Fox ◽  
M. Fernandez ◽  
S. Lappin
Keyword(s):  
Natural Language ◽  
Type Theory ◽  
Lambda Calculus

Research on Sustainable Mining Engineering

2013 ◽  
Vol 340 ◽  
pp. 126-130 ◽  
Author(s):  
Xiao Guang Yue ◽  
Guang Zhang ◽  
Qing Guo Ren ◽  
Wen Cheng Liao ◽  
Jing Xi Chen ◽  
...  
Keyword(s):  
Information Processing ◽  
Natural Language Processing ◽  
Natural Language ◽  
Language Processing ◽  
Social Economy ◽  
Scientific Research ◽  
The Other ◽  
Mining Engineering ◽  
Chinese Information Processing ◽  
Development Tendency

The concepts of Chinese information processing and natural language processing (NLP) and their development tendency are summarized. There are different comprehension of Chinese information processing and natural language processing in China and the other countries. But the work appears to emerge in the study of key point of languages processing. Mining engineering is very important for our country. Though the final task of languages processing is difficult, Chinese information processing has contributed substantially to our scientific research and social economy and it will play an important part for mining engineering in our future.

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