On the Expressive Power of Non-deterministic and Unambiguous Petri Nets over Infinite Words

We prove that ω-languages of (non-deterministic) Petri nets and ω-languages of (nondeterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of ω-languages of (non-deterministic) Turing machines. We also show that it is highly undecidable to determine the topological complexity of a Petri net ω-language. Moreover, we infer from the proofs of the above results that the equivalence and the inclusion problems for ω-languages of Petri nets are ∏21-complete, hence also highly undecidable. Additionally, we show that the situation is quite the opposite when considering unambiguous Petri nets, which have the semantic property that at most one accepting run exists on every input. We provide a procedure of determinising them into deterministic Muller counter machines with counter copying. As a consequence, we entail that the ω-languages recognisable by unambiguous Petri nets are △30 sets.

Ditransitive Construction in English, Hungarian, Turkish, and Indonesian Language

Every language shows a different way of expressing ditransitive construction. Thus, the present study aims to investigate and compare the important elements exhibit in the languages under discussion in constructing ditransitive sentences. This paper is a qualitative study. The data comes from detailed written grammar texts, corpora, and interviews with native language speakers. The results show that the languages play with the word order to weigh the focus of sentences. English and Indonesian language do not apply any case-marking to mark the function of the noun phrase. However, in the basic prototypical ditransitive construction, Hungarian and Turkish languages apply an accusative marker to mark the theme and a dative marker to mark the recipient. On the other hand, the verbs’ affixation also affects the semantic property of the ditransitive verbs in the Indonesian language. It is also revealed that the languages use the same ditransitive construction to express genuine transfer and beneficial transfer.Keywords: ditransitive construction, cognitive grammar, comparative study.

Model theory of monadic predicate logic with the infinity quantifier

This 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.

Bare Root Infinitives in German

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

Admissible Inference Rules and Semantic Property of Modal Logics

Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic 𝐺𝐿 enjoys weak co-cover property iff all given rules are admissible for logic.

Domains of Polarity Items

This article offers a unified theory of the licensing of Negative and Positive Polarity Items (PIs), focusing on the acceptability conditions of PPIs of the some-type, and NPIs of the any-type. It argues that licensing has both a syntactic and a semantic component. On the syntactic side, the acceptability of PIs is checked in constituents; in fact, for any given PI, only some constituents, referred to as `domains', are eligible for the evaluation of that PI. The semantic dimension of licensing consists in the sensitivity of PIs to the monotonicity properties of the syntactic environments they find themselves in. Two pieces of evidence support the semantic dimension of what I call the ‘environment-based’ approach defended here: (i.) PIs are subject to flip-flop and (ii.) certain inferences affect their acceptability by modifying the monotonicity of their environment. A third property, called ‘entanglement’ and so far unnoticed, is described: the acceptability of PIs depends on the acceptability of other PIs in the same syntactic environment. The latter property is exploited to determine what semantic property some is sensitive to: it turns out that, contrary to the consensus among researchers, some is acceptable in the complement of the set of environments in which any is acceptable, and vice versa.

On the left periphery of Spanish indirect interrogatives

Spanish doubly filled complementizer (DFComp) clauses differ from plain embedded questions in a number of respects (availability of discourse-related projections, islandhood, sequence of tenses, licensing of discourse particles). I argue that the contrast is caused by the presence in the left periphery of these clauses of an illocutionary projection (Haegeman 2004, 2006; Coniglio and Zegrean 2012; Woods 2016b) between the leftmost projection, here identified as Haegeman’s (2004) SubP, and the criterial interrogative projections (InterP and QembP). This illocutionary projection prevents syncretism of the clause-typing and the criterial projections, the default option in plain embedded clauses. This not only explains the range of structural phenomena differentiating DFComp clauses and embedded questions, but also a key semantic property of the former, namely their speech-act denotation. Finally, DFComp clauses are compared with plain embedded questions displaying root behavior under first-person matrix subjects and with English inverted embedded questions. Both are shown to pose minimal variants of the structural pattern proposed for DFComp clauses.