On Pregroups, Freedom, and (Virtual) Conceptual Necessity

Pregroups were introduced in (Lambek, 1999), and provide a founda-tion for a particularly simple syntactic calculus. Buszkowski (2001) showed that free pregroup grammars generate exactly the -free context-free lan-guages. Here we characterize the class of languages generable by all pre-groups, which will be shown to be the entire class of recursively enumerable languages. To show this result, we rely on the well-known representation of recursively enumerable languages as the homomorphic image of the inter-section of two context-free languages (Ginsburg et al., 1967). We define an operation of cross-product over grammars (so-called because of its behaviour on the types), and show that the cross-product of any two free-pregroup grammars generates exactly the intersection of their respective languages. The representation theorem applies once we show that allowing ‘empty cat-egories ’ (i.e. lexical items without overt phonological content) allows us to mimic the effects of any string homomorphism.

What Isn’t Obvious about ‘obvious’: A Data-driven Approach to Philosophy of Logic

It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, I propose that systematically searching for patterns of usage in databases of scholarly works, such as JSTOR, can provide new insights into the ways in which the idea that logic is obvious is reflected in logical and philosophical practice, i.e., in the arguments that logicians and philosophers of logic actually make in their published work

Языковая мультивселенная

This paper argues that logic can benefit from a recent trend in linguistics, namely the study of multilingualism. Giving up monolingualism in logic does not necessarily lead to logical pluralism. Often enough pluralism is just a fight for the recognition of one’s own language rather than a plea for a different logic. Once we let go of the monolithic view of language and embrace multilingualism, interesting new avenues appear for logic that are worth exploring. Moreover, not only is it possible to use logic to analyse the multilingual universe, it is also quite revealing to use the linguistic methodology to reflect on the metatheory of logic itself.В статье обсуждается вопрос о том, что полезного логика может для себя найти в современной тенденции в лингвистике изучать явление многоязычия. Отказ от моноязычия в логике не ведёт с необходимостью к логическому плюрализму. Достаточно часто плюрализм — это просто борьба за признание своего собственного языка, нежели довод в пользу иной логики. При отказе от монолитного взгляда на язык и выборе многоязычия для логики открываются новые интересные перспективы, достойные исследования. Кроме того, не только можно использовать логику для анализа многоязычного универсума, но лингвистическая методология может быть применена для описания самой логической метатеории

Aspects of Space

Kracht M. Aspects of Space. The Baltic International Yearbook of Cognition, Logic and Communication. 2015;10(1)

Modelling for changing transitive active imperative sentences to passive imperative sentences with algebraic structure approach

The active imperative sentences often tend to sound harsh. The sentence has a commanding meaning and ends with an exclamation mark. In the Indonesian language, to be more polite, the sentence uses the word politeness and a different sentence structure. These more polite imperative sentences are called passive imperative sentences. Changing an active imperative sentence to a passive imperative sentence can be done mathematically through several stages. These stages are determining the set of word, and the set of word types, using binary operations to obtain the rules for changing the pronoun as an object to subject, determining the rules for substituting active verbs into passive verbs, determining algebraic structures for an active imperative sentence, specifying a set of politeness words, specifying rules for passive imperative sentence, transformation an active imperative sentence into a passive imperative sentence. The change method produces a mathematical model p to construct the more polite imperative sentence

CANDS: A Computational Implementation of Collins and Stabler (2016)

Syntacticians must keep track of the empirical coverages and the inner workings of syntactic theories, a task especially demanding for minimalist syntacticians to perform manually and mentally. We believe that the computational implementation of syntactic theories is desirable in that it not only (a) facilitates the evaluation of their empirical coverages, but also (b) forces syntacticians to specify their inner workings. In this paper, we present CANDS, a computational implementation of Collins AND Stabler (2016) in the programming language Rust. Specifically, CANDS consists of one main library, cands, as well as two wrapper programs for cands, derivck and derivexp. The main library, cands, implements key definitions of fundamental concepts in minimalist syntax from Collins and Stabler (2016), which can be employed to evaluate and extend specific syntactic theories. The wrapper programs, derivck and derivexp, allow syntacticians to check and explore syntactic derivations through an accessible interface

Strange Loops: Phrase-Linking Grammar Meets Kaynean Pronominalization

As shown earlier by Gärtner (2002), linked trees, the graphs used by Phrase-Linking Grammar (Peters & Ritchie 1981) to capture (unbounded) dependencies, can be cyclic under the special condition that two „displaced“ constituents end up as sisters of each other. Such „PLG-loops“ closely match the particular kind of crossing dependency familiar from Bach-Peters sentences. We will show how PLG-loops allow implementing Bach-Peters configurations within the movement-based approach to binding by Kayne (2002). The resulting structures correspond to QR-derived adjunction structures of the kind introduced by May (1985)