Intuitionistic Logic Research Articles

An end-to-end technology management model in cross-border M&A transactions

Subject. This article examines an adapted management model based on the use of end-to-end technologies in key business processes for finding target companies and deciding on the feasibility of implementing mergers and acquisitions. Objectives. The article aims to present an author-developed model for managing end-to-end technologies in cross-border mergers and acquisitions. Methods. For the study, we used empirical and logical constructions, analysis and synthesis, generalization, formalization, systems approach, and the graphic and tabular methods of visualization. Results. The article identifies trends in the use of artificial intelligence in the main elements of the developed management model along with traditional ways of managing mergers and acquisitions. The proposed system management integrator helps use machine learning algorithms and business process controlling to increase the accuracy and efficiency of decisions and maximize the synergy of the buyer and the target company after the implementation of mergers and acquisitions, which is verified using mathematical algorithms and developed indicators for the use of artificial intelligence and big data business process management. Conclusions. The management model of cross-border mergers and acquisitions of companies determines the use of end-to-end technologies to improve the time and quality of management decision-making.

Timely Computation

This paper addresses the question “what is a digital circuit?” in relation to the fundamentally analog nature of actual (physical) circuits. A simple informal definition is given and then formalized in the proof assistant Agda. At the heart of this definition is the timely embedding of discrete information in temporally continuous signals. Once this embedding is defined (in constructive logic, i.e., type theory), it is extended in a generic fashion from one signal to many and from simple boolean operations (logic gates) to arbitrarily sophisticated sequential and parallel compositions, i.e., to computational circuits. Rather than constructing circuits and then trying to prove their correctness, a compositionally correct methodology maintains specification, implementation, timing, and correctness proofs at every step. Compositionality of each aspect and of their combination is supported by a single, shared algebraic vocabulary and related by homomorphisms. After formally defining and proving these notions, a few key transformations are applied to reveal the linearity of circuit timing (over a suitable semiring), thus enabling practical, modular, and fully verified timing analysis as linear maps over higher-dimensional time intervals. An emphasis throughout the paper is simplicity and generality of specification, minimizing circuit-specific definitions and proofs while highlighting a broadly applicable methodology of scalable, compositionally correct engineering through simple denotations and homomorphisms.

The application of fuzzy logic techniques to improve decision making in apparel size

Traditional set theory, or crisp set theory, is built on the concept of crisp sets. These are sets for which the membership of an element within a set is defined as either true or false; in or out; 1 or 0. This construction is extremely useful, as mathematics has shown, but it struggles to model concepts of our world that possess vagueness or uncertainty. Therefore, we explore an expansion of set theory to allow an element to be partially within a set, thus constituting what is known as a fuzzy set. This paper introduces the basic concept of fuzzy sets, which includes fuzzy sets and crisp sets, as well as the operations of a fuzzy set and fuzzy classification systems. Fuzzy logic has been utilized to solve numerous textile-related difficulties, one of which was determining the proper clothing size. In this study, we examined fuzzy logic applications in textiles, such as the construction of fuzzy expert systems and fuzzy logic for predicting clothing size. This research demonstrates that when determining the correct size of clothing, the outcome is heavily reliant on fuzzy logic.

Promoting Elderly Care Sustainability by Smart Village Facilities Integration—Construction of a Public Service Field with Introduction of Fall Posture Monitoring

In recent years, rural communities in China have been actively exploring a novel approach to elderly care that integrates treatment with health preservation. This study aims to contribute to the sustainable development of rural elderly care by introducing smart technology, specifically fall posture monitoring, into public services and facilities within rural communities. The focus of this study is on addressing a critical issue in elderly medical care: the timely feedback and treatment of falls. To begin, we conduct a comprehensive review of the current status and challenges associated with the application of fall posture monitoring technology. Additionally, we examine the environmental factors that contribute to the risk of falls in public spaces for the elderly. These assessments serve as the technical and environmental foundation for developing the proposed service framework. Our research is conducted from two primary perspectives: the supply of service resources that combine treatment with health preservation and the identification of risk factors associated with outdoor public spaces in the community where falls are likely to occur. Data for this study are collected through behavior mapping and field interviews. In conclusion, we present a constructive logic for the development of a public service field that effectively combines treatment with health preservation. This logic encompasses the integration of technology applications, resource coordination, and improvements to the physical environment. The findings from this study provide a scientific basis for the construction of public service fields in “smart villages” and serve as practical references for similar villages striving to adopt this innovative model. By leveraging the insights gained from this research, it is expected that rural communities will be better equipped to address the challenges of elderly care and facilitate the widespread adoption of this integrated care model.

THEORETICAL BACKGROUND OF TRAINING JOURNALISTS

THEORETICAL BACKGROUND OF TRAINING JOURNALISTS

Construction logic of ocean city branding: Based on cultural brand and cultural memory

The current ocean city development is witnessing a “transitional period” amid modernization and globalization. It has become a consensus of urban development to shape urban cultural brand through culture and stimulate the vitality of urban innovation. Previous studies mainly elaborated on the importance of urban cultural brand in urban development from the perspective of urban marketing events and festivals, but few studies focused on the construction of urban cultural brand from a humanistic perspective. Considering basic human needs, and based on Empathy Theory and Cultural Memory Theory, the current study selected Shenzhen, as the sample and adopted case study approach and grounded theory to explore the empathic elements of urban cultural brand construction from the angles of urban cultural brand and cultural memory, to clarify the memory process of urban cultural brand construction, and to explain the supply and demand sides of brand building. The exploration in this study from the dual dimensions of urban cultural supply and human cultural demand aims to provide reference for the development and promotion of ocean city cultural brand in the new era.

Core Type Theory

Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the possibility of using it as a type theory, in the same kind of way intuitionistic logic is often used as a type theory. Our proof system is not Tennant’s own, but it is very closely related, and determines the same consequence relation. The difference, however, matters for our purposes, and we discuss this. We then turn to the question of strong normalization, showing that although Tennant’s proof system for core logic is not strongly normalizing, our modified system is.

Competing for space? A multi-criteria scenario framework intended to model the energy–biodiversity–land nexus for regional renewable energy planning based on a German case study

BackgroundThe need to balance renewable energy supply with biodiversity conservation has become increasingly urgent in light of current climate, energy, and biodiversity crises. However, the development of wind and solar energy often presents trade-offs such as competing for land use and potentially impacting species and habitats. To address these concerns, ‘priority zones’ for bird and bat species have been proposed as spatial designations for early species protection in the regional planning process. However, there are concerns that the areas suitable for wind and solar energy may be limited further, making it difficult to meet state- and regional-specific spatial targets for renewable energy sites.ResultsTo help decision-makers deal with this challenge, a Multi-Criteria Scenario Framework has been developed and analyzed. It involves a habitat model of priority zones for species conservation and techniques from the intuitive logic scenario planning method. Through a regional case study, various planning criteria were analyzed according to scenarios, such as priority zones for species protection, settlement buffers, and forests. The framework indicates how criteria could be balanced to achieve wind energy spatial targets as well as targets for ground-mounted solar energy with the least possible impact. Results show that compared to other planning criteria, species priority zones had limited competition with spatial wind energy targets. Achieving these targets may require minimal adjustments, such as allowing wind energy in 1–3% of completely protected recreational landscapes. To reconcile land use demands in the energy transition, a balance between ‘green’ protected areas is necessary. Additionally, ground-mounted solar energy could replace some of the wind energy spatial targets while also meeting the overall solar development goals.ConclusionsThe framework provides transparency in assessing trade-offs between multiple objectives and helps quantify the ‘costs’ and ‘benefits’ in renewable energy planning. Adapting more flexible planning methods could help resolve the conflict between wind energy and species protection. Joint analysis of the areas needed for wind and solar energy and determining the optimal energy mix are gaining in importance. However, how the benefits of multi-criteria scenarios can be achieved within the confines of preoccupied and siloed organizations remains an ongoing research topic.

A review of strategic planning for dynamic supply chains: Preparing for uncertainty using scenarios

AbstractThis is a book review of Strategic Planning for Dynamic Supply Chains: Preparing for Uncertainty Using Scenarios by Shardul S. Phadnis, Yossi Sheffi, and Chris Caplice (Cham, Switzerland, 226 p, 2022). The book covers three case studies, presented as vignettes, which illustrate three unique applications of a seven‐step approach to scenario planning, modeled after the Intuitive Logics School. The book is aimed at executives and business leaders, as well as academics, and scenario planning practitioners. This review discusses the unique aspects the scenario team brings to the strategic space, the strengths of their pragmatic process, and key elements in practice that are often left out of the larger academic scholarship.

Are logical intuitions only make-believe? Reexamining the logic-liking effect.

An ongoing debate in the literature on human reasoning concerns whether or not the logical status (valid vs. invalid) of an argument can be intuitively detected. The finding that conclusions of logically valid inferences are liked more compared to conclusions of logically invalid ones-called the logic-liking effect-is one of the most prominent pieces of evidence in support of this notion. Trippas et al. (2016) found this logic-liking effect for different kinds of inferences, including conditional and categorical syllogisms. However, all invalid conclusions presented by Trippas et al. (2016) were also impossible given the premises and had a particular structure of surface features-that is, an incongruent atmosphere. We present new data from five preregistered experiments in which we replicate the effect reported by Trippas et al. (2016) for conditional and categorical syllogisms but show that this effect is eliminated when controlling for confounds in surface features. Moreover, we present evidence that there is a demand effect at play, which suggests that people are deliberately considering atmosphere cues of an argument to inform their liking ratings. Taken together, the findings of the present study cast doubt on the existence of logical intuitions. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

A Lindström theorem for intuitionistic first-order logic

We extend the main result of [1] to the first-order intuitionistic logic (with and without equality), showing that it is a maximal (with respect to expressive power) abstract logic satisfying a certain form of compactness, the Tarski union property and preservation under asimulations. A similar result is also shown for the intuitionistic logic of constant domains.

EXTENDED FRAMES AND SEPARATIONS OF LOGICAL PRINCIPLES

AbstractWe aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$ . To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in $\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in $\mathbf {HA}$ . We see several examples which give us separations among omniscience principles.

Definite Formulae, Negation-as-Failure, and the Base-Extension Semantics of Intuitionistic Propositional Logic

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use the operational view of them as provided by uniform proof-search—the proof-theoretic foundation of logic programming (LP)—to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS.

From Epistemic Norms to Logical Rules: Epistemic Models for Logical Expressivists

In this paper I construct a system of semantics for classical and intuitionistic propositional logic based on epistemic norms governing belief expansion. Working in the AGM-framework of belief change, I give a generalisation of Gärdenfors’ notion of belief systems which can be defined without reference to a logical consequence operator by using a version of the Ramsey Test. These belief expansion systems can then be used to define epistemic models which are sound and complete for either classical or intuitionistic propositional logic depending on which of the two notions of epistemic validity, identified by Levi and Arló-Costa, is used. Finally, I offer a discussion on how these results can be understood as providing a model theory within the framework of logical expressivism.

Executability and Connexivity in an Interpretation of Griss

Although the work of G.F.C. Griss is commonly understood as a program of negationless mathematics, close examination of Griss’s work suggests a more fundamental feature is its executability, a requirement that mental constructions are possible only if corresponding mental activity can be actively carried out. Emphasizing executability reveals that Griss’s arguments against negation leave open several types of negation—including D. Nelson’s strong negation—as compatible with Griss’s intuitionism. Reinterpreting Griss’s program as one of executable mathematics, we iteratively develop a pair of bilateral constructive logics and argue for their adequacy as accounts of the propositional basis of Griss’s work. We conclude by observing connexive features exhibited by the two bilateral logics and by investigating the difficulties connexive principles reveal for the development of executable mathematics.

Towards logical foundations for probabilistic computation

The overall purpose of the present work is to lay the foundations for a new approach to bridge logic and probabilistic computation. To this aim we introduce extensions of classical and intuitionistic propositional logic with counting quantifiers, that is, quantifiers that measure to which extent a formula is true. The resulting systems, called cCPL and iCPL, respectively, admit a natural semantics, based on the Borel σ-algebra of the Cantor space, together with a sound and complete proof system. Our main results consist in relating cCPL and iCPL with some central concepts in the study of probabilistic computation. On the one hand, the validity of cCPL-formulae in prenex form characterizes the corresponding level of Wagner's hierarchy of counting complexity classes, closely related to probabilistic complexity. On the other hand, proofs in iCPL correspond, in the sense of Curry and Howard, to typing derivations for a randomized extension of the λ-calculus, so that counting quantifiers reveal the probability of termination of the underlying probabilistic programs.

The Construction of Chinese Metropolitan Area from the Perspective of Politics of Scale: A Case Study of Nanjing Metropolitan Area, China

The spatial political logic of the construction of Chinese metropolitan areas (CMAs) is unique and complex, involving the interaction of power, spatial production, and the construction of political rationality between multiple scales. Taking the representative Nanjing metropolitan area as an example, we use the “material–organizational–discursive” analytical framework of politics of scale theory to analyze the construction logic of CMAs. This study finds the following: (1) In general, the CMA is a high-quality spatial construction resulting from multi-city negotiation, inter-provincial collaboration, and central–territory linkage, and has generally undergone a process of increasing the power of subjects, nested power relations, frequent scale interactions, and complex interest games; among them, planning is not only a scale tool for competing for power, but also an important representation of the results of multiple power games. (2) In terms of the construction of material space, both the delineation of boundaries and the cross-border connection of infrastructure represent rational thinking and stand as two-way choices of the two power subjects in the MA based on the maintenance and expansion of their own spatial development rights. (3) In terms of organizational space construction, CMAs mainly adopt flexible means, with bilateral and multilateral cooperation at the horizontal level, while there is a certain power inequality at the vertical level. (4) In the construction of discursive space, CMAs have experienced increasing construction significance, escalating scale subjects, and overlapping discourse narratives, and the contrast of power relations has also changed. The contribution of this paper is an expansion of the analytical framework of politics of scale based on the division of spatial dimensions, which provides a new perspective for understanding the construction of CMAs, and also helps us to picture Chinese city–regionalism.

A postulate-driven study of logical argumentation

Logical argumentation is a well-known approach to modeling non-monotonic reasoning with conflicting information. In this paper we provide a comprehensive postulate-based study of properties of logical argumentation frameworks and a full characterization of their semantics and inference relations. In this way we identify well-behaved formal argumentative models of drawing logically justified inferences from a given set of possibly conflicting defeasible, as well as strict assumptions. Given some desiderata in terms of rationality postulates, we consider the conditions that an argumentation framework should fulfill for the desiderata to hold. One purpose of this approach is to assist designers to “plug-in” pre-defined formalisms according to actual needs. To this end, we present a classification of argumentation frameworks relative to the types of attacks they implement. In turn, for each class we determine which desiderata are satisfied. Our study is highly abstract, supposing only a minimal set of requirements on the considered underlying deductive systems, and in this way covering a broad range of formalisms, including classical, intuitionistic and modal logics.

On subreducts of subresiduated lattices and some related logics

Abstract Subresiduated lattices were introduced during the decade of 1970 by Epstein and Horn as an algebraic counterpart of some logics with strong implication previously studied by Lewy and Hacking. These logics are examples of subintuitionistic logics, i.e. logics in the language of intuitionistic logic that are defined semantically by using Kripke models, in the same way as intuitionistic logic is defined, but without requiring of the models some of the properties required in the intuitionistic case. Also in relation with the study of subintuitionistic logics, Celani and Jansana get these algebras as the elements of a subvariety of that of weak Heyting algebras. Here, we study both the implicative and the implicative-infimum subreducts of subresiduated lattices. Besides, we propose a calculus whose equivalent algebraic semantics is given by these classes of algebras. Several expansions of these calculi are also studied together with some interesting properties of them.

The function of predicate words in organization of scientific text

The article is devoted to the issues of studying the discursive features of the communication of a scientific text, since the logical train of thought is most clearly traced in it, i.e. semantic connection between the components of a single whole. The subject of the analysis is the characteristics of the functions of predicate words in the organization of a scientific text. The methodological basis of the study was the theoretical work related to communicative linguistics, cognitive linguistics, cognitive logic, text theory, discourse studies, for which the priority is the study of the language as a cognitive mechanism that plays a role in coding and transforming textual information. The emphasis is placed on the fact that the language serves cognition, and the text, therefore, is a product of a purposeful mental and speech activity of a person and an object of reception. A particular attention is paid to the description of the text-forming categories, especially to the category of cohesion, since, as a whole, the text exists precisely due to the combination of the most diverse types of connections. Based on the results of the analysis, it is emphasized that scientific texts differ from other types of texts in a logical construction. It is concluded that the lexical markers are involved in the logical-semantic organization of scientific texts, expressing a certain relationship, in terms of their participation in ensuring the development of thought and the logical coherence of fragments of scientific texts. It was revealed that the logical cores of scientific texts - predicate words connect the text logically on the basis of the semantic valence that is inherent in them.