Might and might not: Children's conceptual development and the acquisition of modal verbs

When a child acquires her first modal verbs, is she learning how to map words in the language she is learning onto innate concepts of possibility, necessity, and impossibility? Or does she also have to construct modal concepts? If the concepts are constructed, does learning to talk about possibilities play a role in the construction process? Exploring this hypothesis space requires testing children's acquisition of modal vocabulary alongside nonverbal tests of their modal concepts. Here we report a study with 103 children from 4;0 through 7;11 and 24 adults. We argue that the data fit best with the hypothesis that acquisition of modal language and development of modal concepts proceed hand-in-hand. However, more research is needed, especially with 3-year-olds.

Incorporating Concreteness in Multi-Modal Language Models with Curriculum Learning

Over the last few years, there has been an increase in the studies that consider experiential (visual) information by building multi-modal language models and representations. It is shown by several studies that language acquisition in humans starts with learning concrete concepts through images and then continues with learning abstract ideas through the text. In this work, the curriculum learning method is used to teach the model concrete/abstract concepts through images and their corresponding captions to accomplish multi-modal language modeling/representation. We use the BERT and Resnet-152 models on each modality and combine them using attentive pooling to perform pre-training on the newly constructed dataset, which is collected from the Wikimedia Commons based on concrete/abstract words. To show the performance of the proposed model, downstream tasks and ablation studies are performed. The contribution of this work is two-fold: A new dataset is constructed from Wikimedia Commons based on concrete/abstract words, and a new multi-modal pre-training approach based on curriculum learning is proposed. The results show that the proposed multi-modal pre-training approach contributes to the success of the model.

Completing the Picture: Complexity of Graded Modal Logics with Converse

A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames has already been established. By “traditional” classes of frames, we mean those characterized by any positive combination of reflexivity, seriality, symmetry, transitivity, and the Euclidean property. In this paper, we fill the gaps remaining in an analogous classification of the graded modal language with graded converse modalities. In particular, we show its NExpTime-completeness over the class of Euclidean frames, demonstrating this way that over this class the considered language is harder than the language without graded modalities or without converse modalities. We also consider its variation disallowing graded converse modalities, but still admitting basic converse modalities. Our most important result for this variation is confirming an earlier conjecture that it is decidable over transitive frames. This contrasts with the undecidability of the language with graded converse modalities.

Algorithmic correspondence and canonicity for possibility semantics

The present paper develops a unified correspondence treatment of the Sahlqvist theory for possibility semantics, extending the results in the work by Yamamoto (2016, Journal of Logic and Computation, 27, 2411–2430) from Sahlqvist formulas to the strictly larger class of inductive formulas and from the full possibility frames to filter-descriptive possibility frames. Specifically, we define the possibility semantics version of the algorithm Ackermann lemma based algorithm (ALBA) and an adapted interpretation of the expanded modal language used in the algorithm. One notable feature of the adaptation of ALBA to possibility frames setting is that the so-called nominal variables, which are interpreted as complete join-irreducibles in the standard setting, are interpreted as regular open closures of ‘singletons’ in the present setting, which is a novelty of the present paper. We prove the soundness of the algorithm with respect to both (the dual algebras of) full possibility frames and (the dual algebras of) filter-descriptive possibility frames, use the algorithm to give an alternative proof to the one in the work by Holliday (2016, Possibility frames and forcing for modal logic. UC Berkeley Working Paper in Logic and the Methodology of Science. URL. http://escholarship.org/uc/item/9v11r0dq) that the inductive formulas are constructively canonical and show that the algorithm succeeds on inductive formulas. We make some comparisons among different semantic settings in the design of the algorithms and fit possibility semantics into this broader picture.

An infinitary axiomatization of dynamic topological logic

Dynamic topological logic ($\textsf{DTL}$) is a multi-modal logic that was introduced for reasoning about dynamic topological systems, i.e. structures of the form $\langle{\mathfrak{X}, f}\rangle $, where $\mathfrak{X}$ is a topological space and $f$ is a continuous function on it. The problem of finding a complete and natural axiomatization for this logic in the original tri-modal language has been open for more than one decade. In this paper, we give a natural axiomatization of $\textsf{DTL}$ and prove its strong completeness with respect to the class of all dynamic topological systems. Our proof system is infinitary in the sense that it contains an infinitary derivation rule with countably many premises and one conclusion. It should be remarked that $\textsf{DTL}$ is semantically non-compact, so no finitary proof system for this logic could be strongly complete. Moreover, we provide an infinitary axiomatic system for the logic ${\textsf{DTL}}_{\mathcal{A}}$, i.e. the $\textsf{DTL}$ of Alexandrov spaces, and show that it is strongly complete with respect to the class of all dynamical systems based on Alexandrov spaces.