Search Results (33)

Kripke semantics for intuitionistic predicate logic $\mathsf{IQC}$ is often viewed as a forcing relation between posets and formulas. In this paper, we further introduce Cohen forcing into semantics. In particular, we use generic filters to interpret the double-negation translations from classical first-order logic to the intuitionistic version. It explains how our method interprets classical theories into constructive ones. In addition, our approach is generalized to Friedman’s A-translation. Consequently, we propose an optimal A-translation that extends the class of theorems that are conserved from a classical theory to its intuitionistic counterpart. Full article

In multi-agent systems, the interactions between autonomous agents within dynamic and uncertain environments are crucial for achieving their objectives. Current research leverages model checking techniques to verify these interactions, with social accessibility relations commonly used to formalize agent interactions. In multi-agent systems that incorporate generalized possibility measures, the quantification, computation, and model checking of trust properties present significant challenges. This paper introduces an indirect model checking algorithm designed to transform social trust under uncertainty into quantifiable properties for verification. A Generalized Possibilistic Trust Interpreted System (GPTIS) is proposed to model and characterize multi-agent systems with trust-related uncertainties. Subsequently, the trust operators are extended based on Generalized Possibilistic Computation Tree Logic (GPoCTL) to develop the Generalized Possibilistic Trust Computation Tree Logic (GPTCTL), which is employed to express the trust properties of the system. Then, a model checking algorithm that maps trust accessibility relations to trust actions is introduced, thereby transforming the model checking of GPTCTL on GPTIS into model checking of GPoCTL on Generalized Possibility Kripke Structures (GPKSs). The proposed algorithm is provided with a correctness proof and complexity analysis, followed by an example demonstrating its practical feasibility. Full article

Golog Tibetan grammaticalizes both evidentiality and egophoricity, but the two categories interact in a constrained way: evidential marking neutralizes the binary egophoric versus non-egophoric contrast. This paper develops LEE (Logic of Evidentiality and Egophoricity), a multi-modal logic that formalizes this interaction. LEE employs operators □_EGO, □_SENS, and □_INF for egophoric, sensory-evidential, and inferential-evidential markers, respectively. The blocking effect is captured by axioms □_σφ → (□_EGOφ ↔ ◇_EGOφ) for σ ∈ {SENS, INF}. This paper establishes soundness, completeness, and decidability for LEE. Three empirical puzzles receive unified explanation: (i) blocking of egophoric vs. non-egophoric contrasts under evidential marking, (ii) semantic bleaching of egophoric morphology in evidential contexts, and (iii) the unidirectional nature of the evidential–egophoric interaction. Full article

If one believes that $2+2=4$, then one also believes that either $2+2=4$ or 971 is a cousin prime number. This follows from doxastic logics based on standard Kripke relational semantics, which validate disjunction introduction for belief. However, this principle does not hold in topic-sensitive semantics. An agent who lacks the concept of a ‘cousin prime number’ may be unable to entertain, and thus unable to believe, any proposition involving that concept. I argue that while disjunction introduction may fail for belief—and for other epistemic states that presuppose belief—it does hold for certain states that do not require belief. In this paper, I focus on the notion of commitment to the truth. Drawing on the concept of logical grounding, I propose formal semantics that preserve the requirement of topic-grasping, but weaken it in a way that allows for a more standard treatment of disjunction. Full article

We present an extension and generalization of Sahlqvist–van Benthem correspondence to the case of distribution-free modal logic, with, or without negation and/or implication connectives. We follow a reductionist strategy, reducing the correspondence problem at hand to the same problem, but for a suitable system of sorted modal logic (the modal companion of the distribution-free system). The reduction, via a fully abstract translation, builds on the duality between normal lattice expansions and sorted residuated frames with relations (a generalization of classical Kripke frames with relations). The approach is scalable and it can be generalized to other systems, with or without distribution, such as distributive modal logic, or substructural logics with, or without additional modal operators. Full article

We consider restricted forms of the algorithmic problem of definability of first-order sentences by propositional formulas with intuitionistic Kripke frames semantics. We demonstrate positive resolutions for classes of intuitionistic Kripke frames based on linear orders and conversely show that a few natural first-order definable classes give rise to undecidable definability problems by applying the model-theoretic in the nature technique of stable classes of Kripke frames. Full article

This paper recounts the author’s reluctant journey of translating Matthew Fuller and Eyal Weizman’s Investigative Aesthetics: Conflicts and Commons in the Politics of Truth into Japanese, a process that turned out to be a mix of philosophical tightrope walking and comedic pratfalls. Along the way, we meet Baumgarten, the original translator who coined the aesthetica nomenclature, Kant, who insists that there can be no such thing as a science of sensibility, and a parade of Japanese translators who took great artistic liberties in rendering an alien term into a complicated language formed by three layers of different writing systems. The author reflects on his coining of a new translation for “aesthetics” in Japanese—Kansei-Jutsu (“Sensibility-Art”)—a term that baffled publishers, thrilled a few cultural studies scholars, and may have earned a side-eye from beauty salons already using “estetikusu” for facials. The translation saga spirals into debates about what “aesthetics” even means, culminating in a bittersweet realisation: translation is less about getting it right and more about sparking delightful, sometimes ridiculous, new ways of thinking. By the end, aesthetics re-emerges as a celebration of difference, proving that even conflicts can create a strange and wonderful commons when approached with an openness to diverse sensibilities. Full article

In this paper, we develop an exact schedulability test and sufficient infeasibility test for fixed-priority scheduling on multiprocessor platforms. We base our tests on presenting real-time systems as a Kripke model for dynamic real-time systems with sporadic non-preemptible tasks running on a multiprocessor platform and an online scheduler using global fixed priorities. This model includes states and transitions between these states, allows us to formally justify a polynomial-time algorithm for an exact schedulability test using the idea of backward reachability. Using this algorithm, we perform the exact schedulability test for the above real-time systems, in which there is one more task than the processors. The main advantage of this algorithm is its polynomial complexity, while, in general, the problem of the exact schedulability testing of real-time systems on multiprocessor platforms is NP-hard. The infeasibility test uses the same algorithm for an arbitrary task-to-processor ratio, providing a sufficient infeasibility condition: if the real-time system under test is not schedulable in some cases, the algorithm detects this. We conduct an experimental study of our algorithms on the datasets generated with different utilization values and compare them to several state-of-the-art schedulability tests. The experiments show that the performance of our algorithm exceeds the performance of its analogues while its accuracy is similar. Full article

In this paper, I argue that there are several different circumstances in which it is rational for human agents not to trust artificial agents (such as ChatGPT). I claim that artificial agents cannot, in principle, be programmed with their own self (nor a simulation of their own self) and, consequently, cannot properly understand the indexicals ‘I’ and ‘me’. It also follows that they cannot take up a first-person point-of-view and that they cannot be conscious. They can understand that agent so-and-so (described in objective indexical-free terms) trusts or is entrusted but cannot know that they are that agent (if they are) and so cannot know that they are trusted or entrusted. Artificial agents cannot know what it means for it to have a normative expectation, nor what it means for it to be responsible for performing certain actions. Artificial agents lack all of the first-person properties that human agents possess, and which are epistemically important to human agents. Because of these limitations, and because artificial agents figure centrally in the trust relation defined in the Buechner–Tavani model of digital trust, there will be several different kinds of circumstances in which it would be rational for human agents not to trust artificial agents. I also examine the problem of moral luck, define a converse problem of moral luck, and argue that although each kind of problem of moral luck does not arise for artificial agents (since they cannot take up a first-person point-of-view), human agents should not trust artificial agents interacting with those human agents in moral luck and converse moral luck circumstances. Full article

Wearable accelerometers are widely used as an ecologically valid and scalable solution for long-term at-home sleep monitoring in both clinical research and care. In this study, we applied a deep learning domain adversarial convolutional neural network (DACNN) model to this task and demonstrated that this new model outperformed existing sleep algorithms in classifying sleep–wake and estimating sleep outcomes based on wrist-worn accelerometry. This model generalized well to another dataset based on different wearable devices and activity counts, achieving an accuracy of 80.1% (sensitivity 84% and specificity 58%). Compared to commonly used sleep algorithms, this model resulted in the smallest error in wake after sleep onset (MAE of 48.7, Cole–Kripke of 86.2, Sadeh of 108.2, z-angle of 57.5) and sleep efficiency (MAE of 11.8, Cole–Kripke of 18.4, Sadeh of 23.3, z-angle of 9.3) outcomes. Despite being around for many years, accelerometer-alone devices continue to be useful due to their low cost, long battery life, and ease of use. Improving the accuracy and generalizability of sleep algorithms for accelerometer wrist devices is of utmost importance. We here demonstrated that domain adversarial convolutional neural networks can improve the overall accuracy, especially the specificity, of sleep–wake classification using wrist-worn accelerometer data, substantiating its use as a scalable and valid approach for sleep outcome assessment in real life. Full article

We introduce De Morgan Heyting logic for Heyting algebras with De Morgan negation (DH-algebras). The variety $\mathcal{DH}$ of all DH-algebras is congruence distributive. The lattice of all subvarieties of $\mathcal{DH}$ is distributive. We show the discrete dualities between De Morgan frames and DH-algebras. The Kripke completeness and finite approximability of some DH-logics are proven. Some conservativity of DH expansion of a Kripke complete superintuitionistic logic is shown by the construction of frame expansion. Finally, a cut-free terminating Gentzen sequent calculus for the DH-logic of De Morgan Boolean algebras is developed. Full article

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. Full article

In this paper, we introduce and study AD-logic, i.e., a system of (hybrid) modal logic that can be used to reason about Aristotelian diagrams. The language of AD-logic, ${\mathcal{L}}_{\mathit{AD}}$, is interpreted on a kind of birelational Kripke frames, which we call “AD-frames”. We establish a sound and strongly complete axiomatization for AD-logic, and prove that there exists a bijection between finite Aristotelian diagrams (up to Aristotelian isomorphism) and finite AD-frames (up to modal isomorphism). We then show how AD-logic can express several major insights about Aristotelian diagrams; for example, for every well-known Aristotelian family A, we exhibit a formula ${\chi }_A\in {\mathcal{L}}_{\mathit{AD}}$ and show that an Aristotelian diagram D belongs to the family A iff ${\chi }_A$ is validated by D (when the latter is viewed as an AD-frame). Finally, we show that AD-logic itself gives rise to new and interesting Aristotelian diagrams, and we reflect on their profoundly peculiar status. Full article

The extension of the (ordinary) institution theory of Goguen and Burstall, known as the theory of stratified institutions, is a general axiomatic approach to model theories where the satisfaction is parameterized by states of models. Stratified institutions cover a uniformly wide range of applications from various Kripke semantics to various automata theories and even model theories with partial signature morphisms. In this paper, we introduce two natural concepts of logical interpolation at the abstract level of stratified institutions and we provide some sufficient technical conditions in order to establish a causality relationship between them. In essence, these conditions amount to the existence of nominals structures, which are considered fully and abstractly. Full article

The Penn Medicine BioBank (PMBB) is an electronic health record (EHR)-linked biobank at the University of Pennsylvania (Penn Medicine). A large variety of health-related information, ranging from diagnosis codes to laboratory measurements, imaging data and lifestyle information, is integrated with genomic and biomarker data in the PMBB to facilitate discoveries and translational science. To date, 174,712 participants have been enrolled into the PMBB, including approximately 30% of participants of non-European ancestry, making it one of the most diverse medical biobanks. There is a median of seven years of longitudinal data in the EHR available on participants, who also consent to permission to recontact. Herein, we describe the operations and infrastructure of the PMBB, summarize the phenotypic architecture of the enrolled participants, and use body mass index (BMI) as a proof-of-concept quantitative phenotype for PheWAS, LabWAS, and GWAS. The major representation of African-American participants in the PMBB addresses the essential need to expand the diversity in genetic and translational research. There is a critical need for a “medical biobank consortium” to facilitate replication, increase power for rare phenotypes and variants, and promote harmonized collaboration to optimize the potential for biological discovery and precision medicine. Full article