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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 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]

We show that intuitionistic propositional logic is Carnap categorical: the only interpretation of the connectives consistent with the intuitionistic consequence relation is the standard interpretation. This holds with respect to the most well-known semantics relative to which intuitionistic logic is sound and complete; among them Kripke semantics, Beth semantics, Dragalin semantics, topological semantics, and algebraic semantics. These facts turn out to be consequences of an observation about interpretations in Heyting algebras. [ABSTRACT FROM AUTHOR]

With mental models based on relational information, the present research shows that the semantics expressed by the relation can determine the structural properties of the constructed model. In particular, we demonstrate a reversal of the classical, well-replicated symbolic distance effect (SDE), as a function of relational semantics. The classical SDE shows that responses are more accurate, and faster, the wider the distance between queried elements on a mentally constructed rank order. We replicate this effect in a study using a relation that expresses a rank hierarchy ("older than," Experiment 4). In contrast, we obtain a clear reversal of the same effect for accuracy data when the relation expresses a number of equivalence classes ("is from the same city," Experiments 1–3). In Experiment 3, we find clear evidence of a reversed SDE for accuracy and latency in the above standard condition, and flat curves of means, across pair distances, for accuracy and latency in a condition that makes equivalence classes salient from the beginning. We discuss these findings in the context of a process model of equivalence class formation based on learned piecemeal information. [ABSTRACT FROM AUTHOR]

Residuated basic logic (RBL) is the logic of residuated basic algebras, which constitutes a conservative extension of basic propositional logic (BPL). The basic implication is a residual of a non-associative binary operator in RBL. The conservativity is shown by relational semantics. A Gentzen-style sequent calculus GRBL , which is an extension of the distributive full non-associative Lambek calculus, is established for residuated basic logic. The calculus GRBL admits the mix-elimination, subformula, and disjunction properties. Moreover, the class of all residuated basic algebras has the finite embeddability property. The consequence relation of GRBL is decidable. [ABSTRACT FROM AUTHOR]

We take Carnap's problem to be to what extent standard consequence relations in various formal languages fix the meaning of their logical vocabulary, alone or together with additional constraints on the form of the semantics. This paper studies Carnap's problem for basic modal logic. Setting the stage, we show that neighborhood semantics is the most general form of compositional possible worlds semantics, and proceed to ask which standard modal logics (if any) constrain the box operator to be interpreted as in relational Kripke semantics. Except when restricted to finite domains, no modal logic characterizes exactly the Kripkean interpretations of $\Box $. Moreover, we show that, in contrast with the case of first-order logic, the obvious requirement of permutation invariance is not adequate in the modal case. After pointing out some known facts about modal logics that nevertheless force the Kripkean interpretation, we focus on another feature often taken to embody the gist of modal logic: locality. We show that invariance under point-generated subframes (properly defined) does single out the Kripkean interpretations, but only among topological interpretations, not in general. Finally, we define a notion of bisimulation invariance—another aspect of locality—that, together with a reasonable closure condition, gives the desired general result. Along the way, we propose a new perspective on normal neighborhood frames as filter frames, consisting of a set of worlds equipped with an accessibility relation, and a free filter at every world. [ABSTRACT FROM AUTHOR]

This article aims at providing some extension of the modal square of opposition in the light of Ockham's account of modal operators. Moreover, we set forth some significant remarks on the de re–de dicto distinction and on the modal operator of contingency by means of a set-theoretic algebra called numbering semantics. This generalization starting from Ockham's account of modalities will allow us to take into consideration whether Ockham's account holds water or not, and in which case it should be changed. [ABSTRACT FROM AUTHOR]

We show that monadic intuitionistic quantifiers admit the following temporal interpretation: "always in the future" (for $\forall $) and "sometime in the past" (for $\exists $). It is well known that Prior's intuitionistic modal logic ${\sf MIPC}$ axiomatizes the monadic fragment of the intuitionistic predicate logic, and that ${\sf MIPC}$ is translated fully and faithfully into the monadic fragment ${\sf MS4}$ of the predicate ${\sf S4}$ via the Gödel translation. To realize the temporal interpretation mentioned above, we introduce a new tense extension ${\sf TS4}$ of ${\sf S4}$ and provide a full and faithful translation of ${\sf MIPC}$ into ${\sf TS4}$. We compare this new translation of ${\sf MIPC}$ with the Gödel translation by showing that both ${\sf TS4}$ and ${\sf MS4}$ can be translated fully and faithfully into a tense extension of ${\sf MS4}$ , which we denote by ${\sf MS4.t}$. This is done by utilizing the relational semantics for these logics. As a result, we arrive at the diagram of full and faithful translations shown in Figure 1 which is commutative up to logical equivalence. We prove the finite model property (fmp) for ${\sf MS4.t}$ using algebraic semantics, and show that the fmp for the other logics involved can be derived as a consequence of the fullness and faithfulness of the translations considered. [ABSTRACT FROM AUTHOR]

Here, I combine the semantics of Mares and Goldblatt [20] and Seki [29, 30] to develop a semantics for quantified modal relevant logics extending ${\bf B}$. The combination requires demonstrating that the Mares–Goldblatt approach is apt for quantified extensions of ${\bf B}$ and other relevant logics, but no significant bridging principles are needed. The result is a single semantic approach for quantified modal relevant logics. Within this framework, I discuss the requirements a quantified modal relevant logic must satisfy to be "sufficiently classical" in its modal fragment, where frame conditions are given that work for positive fragments of logics. The roles of the Barcan formula and its converse are also investigated. [ABSTRACT FROM AUTHOR]

Due to the increasing use of information technologies by biomedical experts, researchers, public health agencies, and healthcare professionals, a large number of scientific literatures, clinical notes, and other structured and unstructured text resources are rapidly increasing and being stored in various data sources like PubMed. These massive text resources can be leveraged to extract valuable knowledge and insights using machine learning techniques. Recent advancement in neural network-based classification models has gained popularity which takes numeric vectors (aka word representation) of training data as the input to train classification models. Better the input vectors, more accurate would be the classification. Word representations are learned as the distribution of words in an embedding space, wherein each word has its vector and the semantically similar words based on the contexts appear nearby each other. However, such distributional word representations are incapable of encapsulating relational semantics between distant words. In the biomedical domain, relation mining is a well-studied problem which aims to extract relational words, which associates distant entities generally representing the subject and object of a sentence. Our goal is to capture the relational semantics information between distant words from a large corpus to learn enhanced word representation and employ the learned word representation for various natural language processing tasks such as text classification. In this article, we have proposed an application of biomedical relation triplets to learn word representation through incorporating relational semantic information within the distributional representation of words. In other words, the proposed approach aims to capture both distributional and relational contexts of the words to learn their numeric vectors from text corpus. We have also proposed an application of the learned word representations for text classification. The proposed approach is evaluated over multiple benchmark datasets, and the efficacy of the learned word representations is tested in terms of word similarity and concept categorization tasks. Our proposed approach provides better performance in comparison to the state-of-the-art GloVe model. Furthermore, we have applied the learned word representations to classify biomedical texts using four neural network-based classification models, and the classification accuracy further confirms the effectiveness of the learned word representations by our proposed approach. [ABSTRACT FROM AUTHOR]

Let a priority micro pluralist be someone who holds that particles or other microscopic objects are fundamental. Rivals to priority micro pluralism include priority monism (the view that the only fundamental concrete object is the entire cosmos) as well as the Aristotelian view that some ordinary macroscopic objects are fundamental. Although priority micro pluralism is popular, I show that it encounters great difficulty in even the most straightforward cases. For example, this tennis ball is spherical; how is this fact to be grounded in facts about the microscopic realm? I consider a number of possible answers to this question. The most promising proposals attempt to exploit the close connection emphasized by Kripke between objects and their original material constituents. I argue that these proposals fail. I conclude that it is worth seriously considering alternatives to this sort of pluralism. [ABSTRACT FROM AUTHOR]

The joint logic of problems and propositions QHC introduced by S. A. Melikhov, as well as intuitionistic modal logic QH4, is studied. An immersion of these logics into classical first-order predicate logic is considered. An analog of the Löwenheim–Skolem theorem on the existence of countable elementary submodels for QHC and QH4 is established. [ABSTRACT FROM AUTHOR]

I show that the logic $\textsf {TJK}^{d+}$ , one of the strongest logics currently known to support the naive theory of truth, is obtained from the Kripke semantics for constant domain intuitionistic logic by (i) dropping the requirement that the accessibility relation is reflexive and (ii) only allowing reflexive worlds to serve as counterexamples to logical consequence. In addition, I provide a simplified natural deduction system for $\textsf {TJK}^{d+}$ , in which a restricted form of conditional proof is used to establish conditionals. [ABSTRACT FROM AUTHOR]

The notion of a critical successor [5] in relational semantics has been central to most classic modal completeness proofs in interpretability logics. In this paper we shall work with a more general notion, that of an assuring successor. This will enable more concisely formulated completeness proofs, both with respect to ordinary and generalised Veltman semantics. Due to their interesting theoretical properties, we will devote some space to the study of a particular kind of assuring labels, the so‐called full labels and maximal labels. After a general treatment of assuringness, we shall apply it to obtain a completeness result for the modal logic ILP$\mathsf {ILP}$ w.r.t. generalised semantics for a restricted class of frames. [ABSTRACT FROM AUTHOR]

This paper aims to show that intuitionistic Kripke models are a powerful tool for interpreting Kant's 'Critical Philosophy'. Part I reviews some old work of mine that applies these models to provide a reading of Kant's second antinomy about the divisibility of matter and to answer several attacks on Kant's antinomies. But it also points out three shortcomings of that original application. First, the reading fails to account for Kant's second antinomy claim that matter is divisible 'ad infinitum' and his first antinomy claim that empirical space extends only 'ad indefinitum'. Secondly, in conformity with the 'assertability' heuristics for Kripke models, it attributes an assertability semantics to Kant. In fact, it attributes a pair of assertability semantics to Kant, but neither of these accords with modern assertabilism. And finally, one must wonder the propriety of using contemporary assertability and contemporary formal logic to save an eighteenth-century text. Part II goes historical to solve the problems about assertability. It outlines the Descartes–Leibniz dialectic about the infinite/indefinite distinction and demonstrates how each position reflects larger philosophical positions. It then demonstrates that Kant's two versions of assertability and his version of the infinite/indefinite dichotomy emerge naturally from his attempts (pre-critical and then critical) to resolve a tension in Leibniz's philosophy. In light of this demonstration, Part III adapts the Kripke model interpretation so that it does reflect that dichotomy. It then refines the Kripke semantics in order to model some of Kant's signature critical doctrines, and it shows how Kant's critical version of the infinite/indefinite distinction differs from all those of his predecessors and from his own pre-critical version. It also addresses the question of using contemporary logical machinery to interpret Kant. Part IV turns the tables and uses what we have learned about Kant and modern semantics in order to address a pair of issues in the contemporary critical foundations of logic. [ABSTRACT FROM AUTHOR]

This paper deals with semilinear extensions of implicational tonoid and partial Galois logics. To this end, first the class of implicational tonoid prelinear logics is defined and it is verified that these logics are semilinear in an algebraic context, namely an implicational tonoid logic is semilinear if it is complete over linearly ordered matrices. Next, a relational semantics is introduced for finitary implicational tonoid prelinear logics and it is proved that these logics are complete on the semantics. Thirdly the term "semilinear" is generalized to a notion to be applied in a set-theoretic context and it is verified that finitary implicational tonoid prelinear logics are semilinear in this context. Finally some extensions satisfying abstract Galois, dual Galois properties are introduced together with similar relational semantics for them and it is shown that these logics are semilinear in both contexts. [ABSTRACT FROM AUTHOR]

Implicational partial Galois logics and some of their semilinear extensions, such as semilinear extensions satisfying abstract Galois and dual Galois connection properties, have been introduced together with their relational semantics. However, similar extensions satisfying residuated, dual residuated connection properties have not. This paper fills the gaps by introducing those semilinear extensions and their relational semantics. To this end, the class of implicational (dual) residuated-connected prelinear gaggle logics is defined and it is verified that these logics are semilinear. In particular, associated with the contribution of this work, we note the following two: One is that implications can be introduced by residuated connection in semilinear logics. This shows that the residuated, dual residuated connection properties are important and so need to be investigated in semilinear logics. The other is that set-theoretic relational semantics can be provided for semilinear logics. Semilinear logics have been dealt with extensively in algebraic context, whereas they have not yet been performed in the set-theoretic one. [ABSTRACT FROM AUTHOR]

The aim of Medical Knowledge Graph Completion is to automatically predict one of three parts (head entity, relationship, and tail entity) in RDF triples from medical data, mainly text data. Following their introduction, the use of pretrained language models, such as Word2vec, BERT, and XLNET, to complete Medical Knowledge Graphs has become a popular research topic. The existing work focuses mainly on relationship completion and has rarely solved entities and related triples. In this paper, a framework to predict RDF triples for Medical Knowledge Graphs based on word embeddings (named PTMKG-WE) is proposed, for the specific use for the completion of entities and triples. The framework first formalizes existing samples for a given relationship from the Medical Knowledge Graph as prior knowledge. Second, it trains word embeddings from big medical data according to prior knowledge through Word2vec. Third, it can acquire candidate triples from word embeddings based on analogies from existing samples. In this framework, the paper proposes two strategies to improve the relation features. One is used to refine the relational semantics by clustering existing triple samples. Another is used to accurately embed the expression of the relationship through means of existing samples. These two strategies can be used separately (called PTMKG-WE-C and PTMKG-WE-M, respectively), and can also be superimposed (called PTMKG-WE-C-M) in the framework. Finally, in the current study, PubMed data and the National Drug File-Reference Terminology (NDF-RT) were collected, and a series of experiments was conducted. The experimental results show that the framework proposed in this paper and the two improvement strategies can be used to predict new triples for Medical Knowledge Graphs, when medical data are sufficiently abundant and the Knowledge Graph has appropriate prior knowledge. The two strategies designed to improve the relation features have a significant effect on the lifting precision, and the superposition effect becomes more obvious. Another conclusion is that, under the same parameter setting, the semantic precision of word embedding can be improved by extending the breadth and depth of data, and the precision of the prediction framework in this paper can be further improved in most cases. Thus, collecting and training big medical data is a viable method to learn more useful knowledge. [ABSTRACT FROM AUTHOR]

For each n ∈ N , we introduce the algebraic semantics for the minimum many-valued modal logic over the MV-chain with n elements. We prove that this quasivariety of algebras is generated by the complex algebras, obtaining as a consequence the completeness result of the logic with respect to the Kripke semantics. As a first step towards the study of this algebraic semantics, we study some congruences of the complex algebras. [ABSTRACT FROM AUTHOR]

Six interesting variants of the logics BN4 and E4--which can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively--were previously developed in the literature. All these systems are related to the family of relevant logics and contain Routley and Meyer's basic logic B, which is well-known to be specifically associated with the ternary relational semantics. The aim of this paper is to develop reduced general Routley-Meyer semantics for them. Strong soundness and completeness theorems are proved for each one of the logics. [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]

The basic quasi-Boolean negation (QB-negation) expansions of relevance logics included in Anderson and Belnap's relevance logic R are defined. We consider two types of QB-negation: H-negation and D-negation. The former one is of paraintuitionistic or superintuitionistic character, the latter one, of dual intuitionistic nature in some sense. Logics endowed with H-negation are paracomplete; logics with D-negation are paraconsistent. All logics defined in the paper are given a Routley-Meyer ternary relational semantics. [ABSTRACT FROM AUTHOR]

It is introduced an immune dynamic n-valued Łukasiewicz logic I D Ł n on the base of n-valued Łukasiewicz logic Ł n and corresponding to it immune dynamic M V n -algebra ( I D L n -algebra), 1 < n < ω , which are algebraic counterparts of the logic, that in turn represent two-sorted algebras (M , R , ◊) that combine the varieties of M V n -algebras M = (M , ⊕ , ⊙ , ∼ , 0 , 1) and regular algebras R = (R , ∪ , ; , ∗) into a single finitely axiomatized variety resembling R-module with "scalar" multiplication ◊ . Kripke semantics is developed for immune dynamic Łukasiewicz logic I D Ł n with application in immune system. [ABSTRACT FROM AUTHOR]

Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Kripke's 'objectual' interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these Quinean worries. Yet there remain residual Quinean worries for epistemic modality. Theorists have recently been toying with assignment-shifting treatments of epistemic contexts. On such views an epistemic operator ends up binding all the variables in its scope. One might worry that this yields the undesirable result that any attempt to 'quantify in' to an epistemic environment is blocked. If quantifying into the relevant constructions is vacuous, then such views would seem hopelessly misguided and empirically inadequate. But a famous alternative to Kripke's semantics, namely Lewis' counterpart semantics, also faces this worry since it also treats the boxes and diamonds as assignment-shifting devices. As I'll demonstrate, the mere fact that a variable is bound is no obstacle to binding it. This provides a helpful lesson for those modelling de re epistemic contexts with assignment sensitivity, and perhaps leads the way toward the proper treatment of binding in both metaphysical and epistemic contexts: Kripke for metaphysical modality, Lewis for epistemic modality. [ABSTRACT FROM AUTHOR]

The aim of this paper is to take a close look at John McGahern's mind style through the language of the heroine Elizabeth Reegan and other characters, in his 1963 novel The Barracks. Specifically, attention will be drawn to how the linguistic choices shape the figurative language to cast the author's controversial views on the religion-pervaded puritan Irish society that he knew so well. This will be done from two different perspectives. One perspective is through the breast cancer afflicted heroine, who asserts herself as a free thinker and a woman of science, in a society where priests have a strong influence at all social levels, and most women settle for housekeeping. The other is also through Elizabeth, together with other minor characters, who dare question some of the basic well-established ideological assumptions, in a series of examples where the author skilfully raises two parallel dichotomies, namely, FAITH versus REASON, and DARKNESS versus LIGHT. At a linguistic level, the present analysis relies on precepts from Frame Semantics, Conceptual Metaphor Theory, and Cognitive Grammar. These insights prove a most useful method of approach to a narrative text while unearthing the author's ideological world view. [ABSTRACT FROM AUTHOR]

This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic. [ABSTRACT FROM AUTHOR]

This paper continues the investigation of the logic of competing theories (be they scientific, social, political etc.) initiated in [4]. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive graphs, inspired by Ploščica's representation of general lattices. We axiomatize the resulting many-valued, non-distributive modal logic of these structures and prove a completeness theorem. We illustrate the application of this logic through a case study in which we model competition among interacting political promises and social demands within an arena of political parties social groups. [ABSTRACT FROM AUTHOR]

The traditional rendering "grace" for חֵן is controversial. Frame semantics, a theory originating in cognitive linguistics, anticipates that prototypical situations are evoked in language users' minds each time a word is used. Thus, a "frame" for " חֵן situations" is reconstructed from Biblical texts. Apart from the basic meaning "beauty" which is offered in dictionaries, too, an extended meaning is presented: חֵן designates "the settling of a (potential) conflict between two parties that only one party can bring to a conclusion." [ABSTRACT FROM AUTHOR]

We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCw. [ABSTRACT FROM AUTHOR]

In her rich paper, Friederike Moltmann provides an extension of standard (= sentence-based) truthmaker semantics that (i) generalizes the familiar truthmaking relation to attitudinal, modal, and intensional objects and that (ii) applies the result of this generalization (called I object-based truthmaker semantics i , hereafter "OTS") to the interpretation of different kinds of mental attitude reports (incl. reports with clause-taking and with intensional transitive verbs). In (20), HT ht is a content-related domain projection function that identifies the propositional content of a content individual (see e.g., [16], [17]). (20) HT

Compliance analysis requires legal counsel but is generally unavailable in many software projects. Analysis of legal text using logic-based models can help developers understand requirements for the development and use of software-intensive systems throughout its lifecycle. We outline a practical modeling process for norms in legally binding agreements that include contractual rights and obligations. A computational norm model analyzes available rights and required duties based on the satisfiability of situations, a state of affairs, in a given scenario. Our method enables modular norm model extraction, representation, and reasoning. For norm extraction, using the theory of frame semantics, we construct two foundational norm templates for linguistic guidance. These templates correspond to Hohfeld's concepts of claim-right and its jural correlative, duty. Each template instantiation results in a norm model, encapsulated in a modular unit which we call a super-situation that corresponds to an atomic fragment of law. For hierarchical modularity, super-situations contain a primary norm that participates in relationships with other norm models. Norm compliance values are logically derived from its related situations and propagated to the norm's containing super-situation, which in turn participates in other super-situations. This modularity allows on-demand incremental modeling and reasoning using simpler model primitives than previous approaches. While we demonstrate the usefulness of our norm models through empirical studies with contractual statements in open source software and privacy domains, its grounding in theories of law and linguistics allows wide applicability. [ABSTRACT FROM AUTHOR]

Taking a cognitive approach to genre-specific language, this corpus-based study investigated the disciplinary and paradigmatic effect on the use of a specific type of attitude markers—surprise markers—with an analytical framework informed by frame semantics. A Surprise frame was generated and then used to analyze the use of surprise markers in a 2,000,000-word corpus consisting of 320 full-length empirical research articles collected from two social sciences (applied linguistics vs. clinical psychology) cutting across two research paradigms (qualitative vs. quantitative). Results from multiple binary logistic regression analyses show that the research paradigm can reliably predict the absence or presence of five categories across four frame elements of the Surprise frame. This study not only extends the application of frame semantics to discourse analysis but also has the potential to create a new direction for research in English for academic purpose. [ABSTRACT FROM AUTHOR]

We introduce fuzzy relational modalities of necessity and possibility designed to handle propositions that can be truth-valueless. We identify several important types of these modalities, corresponding to families of connectives and quantifiers of fuzzy partial logic (Bochvar, Sobociński, Kleene) and show some of their properties. We also present a faithful syntactic translation of the resulting fuzzy partial modal logic to first-order fuzzy partial logic. [ABSTRACT FROM AUTHOR]

Sarah Moss' thesis that we have probabilistic knowledge is from some perspectives unsurprising and from other perspectives hard to make sense of. The thesis is potentially transformative, but not yet elaborated in sufficient detail for epistemologists. This paper interprets Mossean probabilistic knowledge in a suitably-modified Kripke framework, thus filling in key details. It argues that probabilistic knowledge looks natural and plausible when so interpreted, and shows how the most pressing challenges to the thesis can be overcome. Most importantly, probabilistic knowledge can satisfy factivity in the framework, though we are not forced to accept a specific account of probabilistic "facts". The framework also reflects Moss' claim that old-fashioned propositional knowledge is just a limiting case of probabilistic knowledge, and all knowledge is fundamentally probabilistic. Finally, Moss endorses a failure of contraposition: for example, p implies probably p, but not probably p does not imply not p. The framework makes clear the sense in which the valid inferences regarding probably p are as Moss claims. [ABSTRACT FROM AUTHOR]

We shall be concerned with the modal logic BK—which is based on the Belnap–Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding 'strong negation'. Though all four values 'truth', 'falsity', 'neither' and 'both' are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for 'neither' or/and 'both' leads to quite unexpected results. To be more precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics. [ABSTRACT FROM AUTHOR]

The chunking problem is central to linguistics, semiotics, and poetics: How do we learn to organize a language into patterns and to use those patterns creatively? Linguistics has mainly offered two answers, one based on rule inference through innate capacities for processing and the other based on usage and on outstanding capacities for memory and retrieval. Both views are based on induction and compositionality. The Parry–Lord theory of oral composition-in-performance has argued that oral singers produce complex poems out of rehearsed improvisation through the mastery of a system of formulas, chunks that integrate phrasal, metrical, and semantic structures. The framework of formulaic creativity proposed here argues that the cognitive study of oral poetics can provide crucial insights into the chunking problem. I show the major connections between Parry–Lord and usage-based cognitive linguistics, mainly Construction Grammar and Frame Semantics. However, these approaches still remain compositional and thus struggle to model creativity and learning in oral poetry and everyday speech. The alternative is to explore a model of formulaic creativity not based on compositional patterns, but on wide learning for connecting discriminative perceptual features directly to semantic contrasts within a complex dynamic system, without the intermediation of a set of discrete units. [ABSTRACT FROM AUTHOR]

Holmes exists is false. How can this be, when there is no one for the sentence to misdescribe? Part of the answer is that a sentence's topic depends on context. The king of France is bald, normally unevaluable, is false qua description of the bald people. Likewise Holmes exists is false qua description of the things that exist; it misdescribes those things as having Holmes among them. This does not explain, though, how Holmes does not exist differs in cognitive content from, say, Vulcan does not exist. Our answer builds on an observation of Kripke's: even if Holmes exists, he is not in this room, for we were all born too late. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of English motion verbs in the specialized field of adventure tourism and proposes a terminological description of these verbs from a lexico-semantic approach. Motion verbs play a significant role in adventure tourism as they express central actions that are carried out in this domain and connect participants, such as tourists, places and typical instruments to these actions. The analysis aims to reveal how the linguistic properties of these verbs and their interactions with participants contribute to the expression of knowledge. After stating our assumptions and reviewing previous work, the article describes a corpus-based methodology to identify relevant verbs and the different steps taken to implement their description in the DicoAdventure database. The methodology comprises three main steps and is illustrated by applying it to a set of motion verbs extracted from the Advencor corpus. [ABSTRACT FROM AUTHOR]

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan. [ABSTRACT FROM AUTHOR]

We define Kripke semantics for propositional intuitionistic logic with Suszko's identity (ISCI). We propose sequent calculus for ISCI along with cut-elimination theorem. We sketch a constructive interpretation of Suszko's propositional iden- tity connective. [ABSTRACT FROM AUTHOR]

We prove completeness, interpolation, decidability and an omitting types theorem for certain multi-dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach is algebraic addressing varieties generated by complex algebras of Kripke semantics for such logics. The algebras dealt with are common cylindrification free reducts of cylindric and polyadic algebras. For finite dimensions, we show that such varieties are finitely axiomatizable, have the super amalgamation property, and that the subclasses consisting of only completely representable algebras are elementary, and are also finitely axiomatizable in first order logic. Also their modal logics have an N P complete satisfiability problem. Analogous results are obtained for infinite dimensions by replacing finite axiomatizability by finite schema axiomatizability. [ABSTRACT FROM AUTHOR]

Standard reasoning about Kripke semantics for modal logic is almost always based on a background framework of classical logic. Can proofs for familiar definability theorems be carried out using a nonclassical substructural logic as the metatheory? This article presents a semantics for positive substructural modal logic and studies the connection between frame conditions and formulas, via definability theorems. The novelty is that all the proofs are carried out with a noncontractive logic in the background. This sheds light on which modal principles are invariant under changes of metalogic, and provides (further) evidence for the general viability of nonclassical mathematics. [ABSTRACT FROM AUTHOR]

Drawing extends the capacity to communicate, since it allows individuals to use graphic objects and symbols to articulate complex ideas not easily communicated using words alone. Similarly, theorists argue that metaphors are commonly used to communicate complex and abstract concepts. Though, the interpretation of visual metaphors has been studied in relation to film and advertising, referencing common metaphors used in language, research has yet to examine how individuals construct their own visual metaphors and whether existing language-based metaphors are used, as a basis. Studying the underlying structure of drawings, using organizing frameworks and mapping systems, provides insight into how individuals use metaphors to communicate and the interdependent relationships between text and image. This study applies conceptual metaphor theory and frame semantics to identify and map visual metaphors in drawings of Knowledge. Three research questions guided the study: How are visual metaphors [of Knowledge] inferred in participant drawings using existing language-based metaphors?; Can language-based metaphor ontologies and semantic systems be used for interpreting visual metaphors?; and How are inferences found in language-based metaphors evident in the design of visual metaphors? Data were collected as part of the study: What does knowledge look like?, where participants (N = 404) were asked to draw what they thought Knowledge looks like to them, and explain why they drew what they did in writing. Five example cases are presented in the results: 1) the Illuminated Light Bulb, 2) the Electric Brain, 3) the Brain as a Container for Knowledge, 4) Knowledge (Ideas) as Food, and 5) the Open Mind. The findings present three notable conclusions: the combination of multiple metaphors within a single drawing; the use of a language-based metaphor ontology (i.e., Master Metaphor List) and frame semantics as analytic tools to examine visual metaphors; and the potential for additional language-based metaphor categories to emerge. [ABSTRACT FROM AUTHOR]

Graph Neural Networks (GNNs) have received considerable attention in recent years due to their unique ability to model both topologies and semantics in the graphs. In this paper, we explore the use of GNNs in learning low-dimensional node representations in Heterogeneous Information Networks (HINs), which retain rich semantic information across multiple types of nodes and relations. Existing methods for HINs generally focus on modeling heterogeneity at either the node level or the relation level, but not both. As a result, these methods often fall short of optimal performance. To address this issue, we propose a novel Semantic- and Relation-aware Heterogeneous Graph neural Network, dubbed SR-HGN, which jointly incorporates rich semantics preserved on nodes and relations. Our approach involves projecting the HINs into a low-dimensional vector space through two steps: node-level aggregation and type-level aggregation. The node-level aggregation employs an attention mechanism to create relation vectors by aggregating messages from neighborhoods connected via the same type of relation. The type-level aggregation leverages relation vectors to aggregate node representations. In particular, we introduce semantic-aware attention and relation-aware attention in the type-level aggregation to model the contributions of relation vectors, in order to simultaneously gain knowledge from node semantics and relational information. Unlike other approaches that rely on pre-defined meta-paths, our model can be readily applied to most real-world applications without requiring any domain knowledge. To validate the effectiveness of our proposed approach, we conducted extensive experiments on three public datasets. Experimental results demonstrate that the SR-HGN significantly outperforms state-of-the-art baselines on node classification and node clustering tasks. [ABSTRACT FROM AUTHOR]