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The present paper attempts to provide an exact truthmaker semantical analysis of modalized propositions. According to the present proposal, an exact truthmaker for "Necessarily P" is a state that bans every exact truthmaker for "Not P", and an exact truthmaker for "Possibly P" is a state that allows an exact truthmaker for P. Based on this proposal, a formal semantics will be developed; and the soundness and completeness results for a well-known family of the systems of normal modal propositional logic will be established. It shall be seen that the present analysis offers an exactification of the standard Kripke semantics in the sense that it analyzes the accessibility relation between possible worlds in terms of the banning and allowing relations between the constituent states, and thereby gives an account of "truth at a possible world" in terms of exact truthmaking. [ABSTRACT FROM AUTHOR]

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as 'informational entropy'), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same 'modal content'; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks. [ABSTRACT FROM AUTHOR]

The article "Quantification, matching and events" by Richard K. Larson discusses the topic of quantification and matching in natural language semantics. The author explores examples of quantification and argues that the truth conditions of these statements involve matching between different elements. The article proposes that matching in quantification arises from the internal semantic structure of the quantifier and suggests that all quantifiers can be analyzed as having an underlying structure involving injections into events. The author also addresses the role of context, the difference between unbound pronouns and variables bound by existential quantifiers, and different analyses of sentences involving quantification and matching. The text concludes by discussing the connection between quantification, matching, and events, and argues that events, injections, and matching are central to all quantification. The article also explores the need for quantificational states in the semantics of adverbial quantifiers and proposes a neo-Davidsonian approach to understanding quantification. The text discusses semantic rules for quantifiers and provides a framework for understanding quantification in natural language. Finally, the author discusses the topic of quantification in relation to adverbial quantification and argues that all quantifiers involve matching. [Extracted from the article]

We introduce dual counterpart intuitionistic logic (or DCInt): a constructive logic that is a conservative extension of intuitionistic logic, a sublogic of bi-intuitionistic logic, has the logical duality property of classical logic, and also retains the modal character of its interpretation of the connective dual to intuitionistic implication. We define its Kripke semantics along with the corresponding notion of a bisimulation, and then prove that it has both the disjunction property and (its dual) the constructible falsity property. Also, for any class |$ {\mathcal{C}}$| of Kripke frames from our semantics, we identify a condition such that |$ {\mathcal{C}}$| will have the disjunction property if it satisfies the condition. This provides a method for generating extensions of DCInt that retain the disjunction property. [ABSTRACT FROM AUTHOR]

Image-text matching plays an important role in solving the problem of cross-modal information processing. Since there are nonnegligible semantic differences between heterogenous pairwise data, a crucial challenge is how to learn a unified representation. Existing methods mainly rely on the alignment between regional image features and corresponding entity words. However, the regional features in the image are often more concerned with the foreground entity information, and the attribute information of the entities and the relational information are ignored. How to effectively integrate entity-attribute alignment and relationship alignment has not been fully studied. Therefore, we propose a Cross-Modal Semantically Augmented Network for Image-Text Matching (CMSAN), which combines the relationships between entities in the image with the semantics of relational words in the text. CMSAN (1) proposes an adaptive word-type prediction model that classifies the words into four types, i.e., entity word, attribute word, relation word, and unnecessary word. It can align different image features at multiple levels. CMSAN (2) designs a sophisticated relationship alignment module and an entity-attribute alignment module that maximizes the exploitation of the semantic information, which enables the model to have more discriminative power and further improves the matching accuracy. [ABSTRACT FROM AUTHOR]

Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical learning theory fail to account for observed phenomena like the double descent or the impact of relational semantics on generalization error. Motivated by experimental observations of "transductive" double descent in key networks and datasets, we use analytical tools from statistical physics and random matrix theory to precisely characterize generalization in simple graph convolution networks on the contextual stochastic block model. Our results illuminate the nuances of learning on homophilic versus heterophilic data and predict double descent whose existence in GNNs has been questioned by recent work. We show how risk is shaped by the interplay between the graph noise, feature noise, and the number of training labels. Our findings apply beyond stylized models, capturing qualitative trends in real-world GNNs and datasets. As a case in point, we use our analytic insights to improve performance of state-of-the-art graph convolution networks on heterophilic datasets. [ABSTRACT FROM AUTHOR]

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named implicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. p ⇒ q is thus defined as ¬ ◊ (p ∧ ¬ q) ∧ ◊ p ∧ ◊ ¬ q . We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle's theses and weak Boethius' thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. [ABSTRACT FROM AUTHOR]

The present paper establishes systematic connections among the first-order correspondents of Sahlqvist modal reduction principles in various relational semantic settings, including crisp and many-valued Kripke frames, and crisp and many-valued polarity-based frames (aka enriched formal contexts). Building on unified correspondence theory, we aim at introducing a theoretical environment which makes it possible to: (a) compare and inter-relate the various frame correspondents (in different relational settings) of any given Sahlqvist modal reduction principle; (b) recognize when first-order sentences in the frame-correspondence languages of different types of relational structures encode the same "modal content"; (c) meaningfully transfer and represent well known relational properties such as reflexivity, transitivity, symmetry, seriality, confluence, density, across different semantic contexts. These results can be understood as a first step in a research program aimed at making correspondence theory not just (methodologically) unified, but also (effectively) parametric. [ABSTRACT FROM AUTHOR]

Dependency trees reflect rich structural information, which can effectively guide models to understand text semantics and are widely used for relation extraction. However, existing dependency-based models suffer from noise in dependency trees, which distorts the modeling of contextual information, particularly when introducing dependency types, further exacerbating the propagation and accumulation of errors. In addition, rule-based pruning strategies used to eliminate noise in dependency trees may lose crucial information for capturing relational patterns, whereas unconstrained learning-based pruning strategies may introduce more noisy edges. These two aspects of dependency trees may cause models to produce semantic confusion, which is detrimental to relation extraction. In this study, we propose a Contextual Dependency-Aware Graph Convolutional Network (C-DAGCN) that works on complete dependency trees and perceives the importance of word dependencies from multiple angles without considering the noise in dependency trees. This study includes three parts. First, the sequence model captures semantic information for the input sentence and its words. We considered the appropriate outputs as word and sentence-level representations based on model characteristics. Second, the structure model enhances the description of the sentence structure and its guidance. We consider that position knowledge implies associations between words; therefore, we propose the Current Word Global Relative Position Knowledge (CW-GRPK) to globally enhance text structure modeling and reduce the models' overreliance on single noisy structure guidance. A dependency-aware module weighs heuristic syntactic knowledge and non-heuristic CW-GRPK to capture fine-grained word-level interactions that effectively distinguish words related to relational semantics. Subsequently, a dependency-guided module, based on the results of the dependency-aware layer, encodes a knowledge-enhanced word graph without losing global linguistic patterns. Third, we constructed high-level linguistic representations based on the results of the sequence and structure model in C-DAGCN as a relational representation and mapped it to the relational decision space for relational prediction. The experimental results demonstrate that our method outperforms nine strong baseline models on two benchmark datasets. Compared with the best baseline Attentive Graph Convolutional Networks (A-GCN) model (Tian et al., 2021), our proposed C-DAGCN model with 90.15 macro-average F1 and 79.52 micro-average F1 achieves 0.28 macro-average F1 and 0.47 micro-average F1 improvement on the SemEval2010-Task8 and ACE2005 datasets, respectively. 1 1 Our code is available at https://github.com/dymyyc/RE%5fC-DAGCN. The released code when run produces results which are the same as those reported in this paper. • A kind of position knowledge globally enhances text structure modeling. • A dependency-aware module captures fine-grained word-level interactions. • Our model constructs a high-level linguistic representation for relation extraction. • Our model outperforms nine strong baselines on the two benchmark datasets. [ABSTRACT FROM AUTHOR]

We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka duality for meet-semilattices. We introduce the notion of Π 1 -persistence and show that every weak positive modal logic is Π 1 -persistent. This approach leads to a new relational semantics for weak positive modal logic, for which we prove an analogue of Sahlqvist's correspondence result.1 [ABSTRACT FROM AUTHOR]