Modal Operators Research Articles

A comparative study of thematic choices and thematic progression patterns in human-written and AI-generated texts

By adopting systemic functional grammar as the theoretical framework, the present research investigates the choices of the textual, the interpersonal, the topical Themes, and thematic progression patterns in human-written and AI-generated argumentative texts to examine how the human author and the robot organize the clause and text. The findings suggest that human-written and AI-generated texts differ significantly in using the subtypes of textual, interpersonal, and marked topical Themes. In terms of textual Themes, the machine tends to use more concession signals to repeat information that has been stated earlier, adopt fewer condition signals since the robot may be less likely to imagine possible or impossible situations, and repetitively rely on clause-initial conjunctive adjuncts of addition to extend the clause to the previous text. As for interpersonal Themes, the robot seldom adopts modal adjuncts or modal verbal operators as interpersonal Themes, which may suggest its lack of awareness of interaction with the reader and its avoidance of expressing its viewpoints in a typical or congruent way. Regarding topical Themes, the less use of marked themes in AI-generated texts demonstrates that AI may less carefully plan the development of the text to foreground the setting or construct coherent text. Considering thematic progression patterns, the frequent use of the constant pattern in AI-generated texts prevents the text from development and makes the text redundant and simplistic like a list of ideas.

Application of Fuzzy Reasoning with Fusion Rules in Intelligent Information Processing

The core of artificial intelligence (AI) research is intelligent information processing, and fuzzy reasoning and fuzzy neural networks are significant research areas in models of intelligent information processing. The study examines the robustness of fuzzy reasoning by using the property characteristics of triangular modal operators and implication operators, which are used to analyse the Lipschitz property of fuzzy operators and its corresponding property characteristics of triangular modal operators and implication operators. Inference operators are used to investigate the robustness and error-control capabilities of fuzzy operators for fuzzy reasoning. The results showed that the robustness of quasi-copula fuzzy reasoning with fusion rules is better, and the corresponding maximum output perturbation is lowest at 0.36 when the fuzzy operator is T[Formula: see text]&R[Formula: see text] and the corresponding maximum output error is lowest at 0.41 when the fuzzy operators are T[Formula: see text]&R[Formula: see text] and T[Formula: see text]&R[Formula: see text]. This shows the optimal performance of the fuzzy associative memory model with fuzzy rule for quasi-copula fuzzy operators and can improve the theoretical technology. The best-performance fuzzy copula operator of the fuzzy associative memory model can enhance the theoretical foundation and technical support for the processing of intelligent information.

Research on Indirect Influence-Line Identification Methods in the Dynamic Response of Vehicles Crossing Bridges

The bridge influence line can effectively reflect its overall structural stiffness, and it has been used in the studies of safety assessment, model updating, and the dynamic weighing of bridges. To accurately obtain the influence line of a bridge, an Empirical and Variational Mixed Modal Decomposition (E-VMD) method is used to remove the dynamic component from the vehicle-induced deflection response of a bridge, which requires the preset fundamental frequency of the structure to be used as the cutoff frequency for the intrinsic modal decomposition operation. However, the true fundamental frequency is often obtained from the picker, and the testing process requires the interruption of traffic to carry out the mode decomposition. To realize the rapid testing of the influence lines of bridges, a new method of indirectly identifying the operational modal frequency and deflection influence lines of bridge structures from the axle dynamic response is proposed as an example of cable-stayed bridge structures. Based on the energy method, an analytical solution of the first-order frequency of vertical bending is obtained for a short-tower cable-stayed bridge, which can be used as the initial base frequency to roughly measure the deflection influence line of the cable-stayed bridge. The residual difference between the deflection response and the roughly measured influence line under the excitation of the vehicle is operated by Fast Fourier Transform, from which the operational fundamental frequency identification of the bridge is realized. Using the operational fundamental frequency as the cutoff frequency and comparing the influence-line identification equations, the empirical variational mixed modal decomposition, and the Tikhonov regularization to establish a more accurate identification of the deflection influence line, the deflection influence line is finally identified. The accuracy and practicality of the proposed method are verified by real cable-stayed bridge engineering cases. The results show that the relative error between the recognized bridge fundamental frequency and the measured fundamental frequency is 0.32%, and the relative error of the recognized deflection influence line is 0.83%. The identification value of the deflection influence line has a certain precision.

Epistemic Logics for Relevant Reasoners

We present a neighbourhood-style semantic framework for modal epistemic logic modelling agents who process information using relevant logic. The distinguishing feature of the framework in comparison to relevant modal logic is that the environment the agent is situated in is assumed to be a classical possible world. This framework generates two-layered logics combining classical logic on the propositional level with relevant logic in the scope of modal operators. Our main technical result is a general soundness and completeness theorem.

Simplified semantics for further relevant logics II

It is shown how to model propositional constants within the simplified Routley-Meyer semantics. Various axioms and rules allowing the definition of modal operators, implicative negations, enthymematical conditionals, and propositions expressing various infinite conjunctions and disjunctions are set forth and shown to correspond to specific frame conditions. Two propositional constants which are both often designated as “the Ackermann constant” are shown to capture two such “infinite” propositions: The conjunction of every logical law and the conjunction of every truth –what Anderson and Belnap called the “world” constant.

Modal weak Kleene logics: axiomatizations and relational semantics

Abstract Weak Kleene logics are three-valued logics characterized by the presence of an infectious truth-value. In their external versions, as they were originally introduced by Bochvar [4] and Halldén [30], these systems are equipped with an additional connective capable of expressing whether a formula is classically true. In this paper we further expand the expressive power of external weak Kleen logics by modalizing them with a unary operator. The addition of an alethic modality gives rise to the two systems $\textsf{B}_{\text{e}}^{\square }$ and $\textsf{PWK}^{\Box }_{\text{e}} $, which have two different readings of the modal operator. We provide these logics with a complete and decidable Hilbert-style axiomatization w.r.t. a three-valued possible worlds semantics. The starting point of these calculi are new axiomatizations for the non-modal bases $\textsf{B}_{\text{e}}$ and $\textsf{PWK}_{\text{e}}$, which we provide using the recent algebraization results about these two logics. In particular, we prove the algebraizability of $\textsf{PWK}_{\text{e}}$. Finally some standard extensions of the basic modal systems are provided with their completeness results w.r.t. special classes of frames.

Subintuitionistic logics and their modal companions: a nested approach

In the present paper we deal with subintuitionistic logics and their modal companions. In particular, we introduce nested calculi for subintuitionistic systems and for modal logics in the S 5 modal cube ranging from K to S 4 . The latter calculi differ from standard nested systems, as there are multiple rules handling the modal operator. As an upshot, we get a purely syntactic proof of the Gödel-McKinsey-Tarski embedding which preserves the structure and the height of the derivations. Finally, we obtain a conservativity result for classical logic over a weak subintuitionistic system.

HYPNOINDUCTORS OF THE EFFECTIVE FORMULA OF POSITIVATION IN SOCIAL ADVERTISING DISCOURSE

The article is devoted to influential elements of social advertising discourse, where Milton-model inductions are arranged, which is proposed to be nominated as hypnoinducers. The purpose of the study was to identify actual hypnoinducers of the influential formula of positivity in social advertising discourse. The object of intelligence research is Ukrainian advertising megadiscourse, the subject is suggestive markers of Ukrainian social advertising discourse. General scientific methods contributed to the delineation of specific features of social advertising discourse, various types of hypnoinducers (descriptive method); identification of the components of a communicative suggestion and combining them into a whole (methods of analysis and synthesis); concretization of general conclusions (method of induction); construction of formula models of advertising influence (modeling method). Special linguistic — the study of the semantic load and functional features of linguistic components of social advertising discourse (contextualinterpretive and component analysis) and the communicative nature of advertising suggestogens (elements of discursive analysis). The methodological base of the latest scientific directions (suggestive linguistics and neurolinguistic programming) made it possible to differentiate and systematize relevant markers (hypnoinducers) of advertising suggestion (methods of meta- and Milton-model identification and suggestive qualification, which are distinguished by R. Bandler, J. Grinder, M. Erikson, T. Yu. Kovalevska. The formulas of vectors of emotional orientation of influence are presented: positivity, negation and change of vector (in commercial, political and social advertising discourses), where special attention is paid to the formula of positivity realized in social advertising discourse. Relevant hypnoinducers, which are fixed in the above formula. In particular, hypnoinducers of complex syntactic structure + lexical-semantic hypnoinductors ("point" markers) and actually lexical-semantic hypnoinducers are singled out. Truisms can act as hypnoinducers of complex syntactic structure; pattern break; "reading thoughts" complicated by other hypnoinducers, and quotations, or "quotes" of an established and transformed structure, which, in turn, often act as separate hypnoinducers without the support of lexical and semantic markers. Elements of the inverse metamodel of the processes of omission (nominalization, nonspecific vocabulary) and generalization (universal quantifiers, modal operators of necessity) act as lexical-semantic hypnoinducers. The characteristic feature is the presence of affectives as super (powerful) hypnoinducers, the presence of ergonomics varies, and predicates are not clearly represented. Prospects for research development: in-depth analysis and systematization of current hypnoinducers in various genres of advertising discourse, which will expand the spectrum of the most effective influential dominants.

A brief note on intuitionistic fuzzy operators

The research on intuitionistic fuzzy sets gives an extra dimension in mathematics. It has been observed that some operators including the modal operators have very interesting properties in intuitionistic fuzzy sets. More important properties are investigated in this paper and new findings are obtained and proved.

An Analysis on Recent Approaches for Image Captioning

Image captioning is an interdisciplinary area that uses techniques from computer vision and natural language processing to provide a textual description of a picture. The Image captioning task is the process of understanding the scene present in the image by identifying objects and associated actions present to create a meaningful human-like caption which can be used for wide range of applications, including image retrieval, video indexing, assistive technology for the visually impaired, content-based image search, biomedicine, and autonomous cars. Formerly, Machine Learning was utilized for this purpose which will be extensive use of hand-crafted features such as Scale-Invariant Feature Transform (SIFT), Local Binary Patterns (LBP), the Histogram of Oriented Gradients (HOG), and combinations of these features. Extracting handmade characteristics from huge datasets is not straightforward or viable. Many deep learning-based techniques were later proposed. Deep Learning retrieval and template-based approaches were presented; however, both had drawbacks such as losing crucial objects. Recent breakthroughs in deep learning and natural language processing have resulted in considerable increases in image captioning system performance which involves adopting attention mechanisms, transformer-based architectures, multi modal connections, Object-Detection based encoder-decoder and many others. In this survey will explore some of the most recent techniques for image captioning, the datasets and evaluation measures that have been employed in deep learning-based automatic image captioning. The ultimate intention of this study is to act as a guide for researchers by emphasizing future directions for research work. Index Terms: image captioning, computer vision, deep learning, Textual description, natural language processing.

Modal algebra of multirelations

Abstract We formalize the modal operators from the concurrent dynamic logics of Peleg, Nerode and Wijesekera in a multirelational algebraic language based on relation algebras and power allegories, using relational approximation operators on multirelations developed in a companion article. We relate Nerode and Wijesekera’s box operator with a relational approximation operator for multirelations and two related operators that approximate multirelations by different kinds of deterministic multirelations. We provide an algebraic soundness proof of Goldblatt’s axioms for concurrent dynamic logic and one for a multirelational Hoare logic based on Nerode and Wijesekera’s box as applications.

Register-based distribution of expressions of modality in COCA

This research scrutinizes expressions of modality at both word and clause ranks. Expressions at the former rank encompass modal verbal operators, modal adjuncts, and modal nominalizations, and expressions at the latter rank encompass ‘explicit subjective’ orientation such as I think and ‘explicit objective’ orientation, such as it is possible. These latter expressions are designated as interpersonal metaphors of modality within the framework proposed by Halliday. Previous studies delimited the distribution of expressions of modality either at word rank or at clause rank; in addition, they undertheorized the relationship between this distribution of modality and formality of registers because the register is testified to be an influential factor in the distribution of expressions of modality. This study, drawing on such statistical methods as variation analysis and correlation analysis, explored the distribution of expressions of modality at both word and clause ranks across registers with different degrees of formality by employing the Corpus of Contemporary American English (COCA). The findings are summarized as follows. First, registers in COCA employ expressions of modality with low and/or median values to judge the proposition at issue for the purpose of entertaining other varying voices. Second, in more formal registers, language users seem to prefer modal nominalizations to modal verbal operators and modal adjuncts at word rank, and ‘explicit objective’ orientation to ‘explicit subjective’ orientation at clause rank. In doing so, they could efficiently conceal the commentators’ subjective meaning, and thus, the objectivity of propositions is highlighted. This study will shed light on the full understanding of the distribution of expressions of modality across registers and the application of such theory as interpersonal metaphor of modality in SFL.

A New Approach of Complex Fuzzy Ideals in BCK/BCI-Algebras

The concept of complex fuzzy sets, where the unit disk of the complex plane acts as the codomain of the membership function, as an extension of fuzzy sets. The objective of this article is to use complex fuzzy sets in BCK/BCI-algebras. We present the concept of a complex fuzzy subalgebra in a BCK/BCI-algebra and explore their properties. Furthermore, we discuss the modal and level operators of these complex fuzzy subalgebras, highlighting their importance in BCK/BCI-algebras. We study various operations, and the laws of a complex fuzzy system, including union, intersection, complement, simple differences, and bounded differences of complex fuzzy ideals within BCK/BCI-algebras. Finally, we generate a computer programming algorithm that implements our complex fuzzy subalgebras/ideals in BCK/BCI-algebras procedure for ease of lengthy calculations.

Determinism of multirelations

Binary multirelations allow modelling alternating nondeterminism, for instance, in games or nondeterministically evolving systems interacting with an environment. Such systems can show partial or total functional behaviour at both levels of alternation, so that nondeterministic behaviour may occur only at one level or both levels, or not at all. We study classes of inner and outer partial and total functional multirelations in a multirelational language based on relation algebra and power allegories. While it is known that general multirelations do not form a category, we show in the multirelational language that the classes of deterministic multirelations mentioned form categories with respect to Peleg composition from concurrent dynamic logic, and sometimes quantaloids. Some of these categories are isomorphic to the category of binary relations. We also introduce determinisation maps that approximate multirelations either by binary relations or by deterministic multirelations. Such maps are useful for defining modal operators on multirelations.

Maximality and modality in infinitival Wh-complements

Infinitival Wh-complements exhibit a modal interpretation, which arises despite there being no overt lexical modal. In the only comprehensive analysis of the modality, Bhatt (1999) argues that it should be attributed to a covert modal operator. The semantics of this operator is more specific than the typical Kratzerian one. This paper reexamines the original motivation underpinning Bhatt's analysis of the covert modal, and argues that such facts can be accounted for if the interrogative component of infinitival Wh-complements is specified to denote only maximal answers – a solution that is needed more generally in the interpretation of questions. Thus, it is not necessary to imbue the covert modal with a more specific semantics, making it possible to more broadly unify modal Wh-questions and infinitival Wh-complements.

Remark on Intuitionistic Fuzzy Temporal Modal Topological Structures

In a series of papers, we have discussed the concept of a modal topological structure modified, extended and illustrated by examples from intuitionistic fuzzy sets. Here, the concept of a temporal modal topological structure is introduced and illustrated with four different intuitionistic fuzzy temporal modal topological structures. These structures are based on intuitionistic fuzzy topological, temporal and modal operators. They are extensions of the temporal topological structures as well as of the modal topological structures.

Satisfiability Threshold of Random Propositional S5 Theories

Modal logic S5, which isan important knowledge representation and reasoning paradigm, has been successfully applied in various artificial-intelligence-related domains. Similar to the random propositional theories in conjunctive clause form, the phase transition plays an important role in designing efficient algorithms for computing models of propositional S5 theories. In this paper, a new form of S5 formula is proposed, which fixes the number of modal operators and literals in the clauses of the formula. This form consists of reduced 3-3-S5 clauses of the form l1∨l2∨ξ, where ξ takes the form □(l3∨l4∨l5), ◊(l3∧l4∧l5), or a propositional literal, and li(1≤i≤5) is a classical literal. Moreover, it is demonstrated that any S5 formula can be translated into a set of reduced 3-3-S5 clauses while preserving its satisfiability. This work further investigates the probability of a random 3-c-S5 formula with c=1,2,3 being satisfied by random assignment. In particular, we show that the satisfiability threshold of random 3-1-S5 clauses is −ln2(1−Pd−Ps)ln78+Ps·ln34, where Ps and Pd denote the probabilities of different modal operators appearing in a clause. Preliminary experimental results on random 3-1-S5 formulas confirm this theoretical threshold.

Complexity of Credulous and Skeptical Acceptance in Epistemic Argumentation Framework

Dung’s Argumentation Framework (AF) has been extended in several directions. Among the numerous proposed extensions, three of them seem to be of particular interest and have correlations between them. These extensions are: constrained AF (CAF), where AF is augmented with (strong) constraints; epistemic AF (EAF), where AF is augmented with epistemic constraints; and incomplete AF (iAF), where arguments and attacks can be uncertain. While the complexity and expressiveness of CAF and iAF have been studied, that of EAF has not been explored so far. In this paper we investigate the complexity and expressivity of EAF. To this end, we first introduce the Labeled CAF (LCAF), a variation of CAF where constraints are defined over the alphabet of labeled arguments. Then, we investigate the complexity of credulous and skeptical reasoning and show that: i) EAF is more expressive than iAF (under preferred semantics), ii) although LCAF is a restriction of EAF where modal operators are not allowed, these frameworks have the same complexity, iii) the results for LCAF close a gap in the characterization of the complexity of CAF. Interestingly, even though EAF has the same complexity as LCAF, it allows modeling domain knowledge in a more natural and easy-to-understand way.

Quintic fuzzy sets: A new class of fuzzy sets for solving multi-criteria decision-making problems under uncertainty

This study proposes a new class of fuzzy sets called Quintic Fuzzy Set (QuFS), where the sum of the fifth power of the membership degree and non-membership degree is less than or equal to one. We introduce the complement operator and basic operations on QuFS and further develop various theorems based on these fundamental set operations. We also present the standard modal operators on QuFS and discuss its elementary properties. We then define a novel score and accuracy function for ranking QuFS, as well as the Euclidean and Hamming distances between two QuFSs. A supplier selection example is presented in detail to illustrate the viability and utility of the proposed QuF-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method. We also present a multi-criteria decision-making (MCDM) problem on COVID-19 lab selection to perform a comparative analysis of QuFS with Fermatean Fuzzy Set (FFS) and Pythagorean Fuzzy Set (PFS). Furthermore, we demonstrate an existing real case study on selection of Health care waste treatment (HCWT) technique in India and perform a comparative analysis with TOPSIS, SAW (Simple Additive Weighting) and WASPAS (Weighted Aggregated Sum Product Assessment) MCDM methods in QuF framework. With the advent of QuFS, a decision-maker can now employ the fuzzy notion to manage complicated and uncertain human judgements. The comparative results indicate that the suggested QuF measures and QuF MCDM technique outperform other fuzzy concepts regarding effectiveness and validity. Due to the restrictive nature of the current fuzzy set theories, the decision-makers in some complex, uncertain real-life problems are not free to choose the degree of membership and non-membership of their choice. Compared to the Intuitionistic Fuzzy Set (IFS), PFS, and FFS, the QuFS developed in this study has a bigger space grade space. This feature of QuFS enables decision-makers to structure complex, uncertain circumstances with greater flexibility in terms of membership and non-membership degrees.

☐ and ◇ in eight-valued non-deterministic semantics for modal logics

Abstract In this paper we study several extensions of the minimal modal logic M. This minimal modal logic is formulated in the language of classical propositional logic together with two modal operators $\Box $ and $\Diamond $, which have no deductive power. By extending the Hilbert calculus for M with various axioms for $\Box $ and $\Diamond $ and/or the rule of necessitation, we obtain several well-known normal modal logics, as well as systems that are of pure theoretical interest. Those systems are shown to be sound and complete wrt to eight-valued semantics. Those semantics are obtained by refinements of an eight-valued semantics for M. Furthermore, we will briefly discuss some limitations of the method presented in this article.