We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the (...) broken-cut modality, and that he was led to analyze constructions of knowledge in the style of epistemic logic. (shrink)

This article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The (...) transitional systems of the algebra of the copula that Peirce develops since 1880 paved the way to the 1896 graphical system of the alpha graphs. It is shown how the rules of the alpha system reinterpret Boolean algebras, answering Peirce’s statement that logical graphs supply a new system of fundamental assumptions to logical algebra. A proof-theoretic analysis is given for the connection betweenPCand the alpha system. (shrink)

Every Berman’s variety \ which is the subvariety of Ockham algebras defined by the equation \ and \) determines a finitary substitution invariant consequence relation \. A sequent system \ is introduced as an axiomatization of the consequence relation \. The system \ is characterized by a single finite frame \ under the frame semantics given for the formal language. By the duality between frames and algebras, \ can be viewed as a \-valued logic as it is characterized by a (...) distributive lattice of \ elements with a unary operator. Moreover, a structural-rule-free, cut-free and terminating sequent system \ is established for \. The Craig interpolation property of \ is shown proof-theoretically utilizing \. (shrink)

We present a dynamic approach to Peirce’s original construal of abductive logic as a logic of conjecture making, and provide a new decidable, contraction-free and cut-free proof system for the dynamic logic of abductive inferences with neighborhood semantics. Our formulation of the dynamic logic of abduction follows the philosophical and scientific track that led Peirce to his late, post-1903 characterization of abductive conclusions as investigands, namely invitations to investigate propositions conjectured at the level of pre-beliefs.

A deterministic weakening \ of the Belnap–Dunn four-valued logic \ is introduced to formalize the acceptance and rejection of a proposition at a state in a linearly ordered informational frame with persistent valuations. The logic \ is formalized as a sequent calculus. The completeness and decidability of \ with respect to relational semantics are shown in terms of normal forms. From an algebraic perspective, the class of all algebras for \ is described, and found to be a subvariety of Berman’s (...) variety \. Every linearly ordered frame is logically equivalent to its dual algebra. It is proved that \ is the logic of a nine-element distributive lattice with a negation. Moreover, \ is embedded into \ by Glivenko’s double-negation translation. (shrink)

Charles Peirce’s alpha system \ is reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of \ is given in terms of two embedding theorems: the system \ and Brünnler’s deep inference system for classical propositional logic can be embedded into each other; and the system \ and Gentzen sequent calculus \ can be embedded into each other.

The minimal weakening \ of Belnap-Dunn logic under the polarity semantics for negation as a modal operator is formulated as a sequent system which is characterized by the class of all birelational frames. Some extensions of \ with additional sequents as axioms are introduced. In particular, all three modal negation logics characterized by a frame with a single state are formalized as extensions of \. These logics have the finite model property and they are decidable.

In the present paper, we start studying epistemic updates using the standard toolkit of duality theory. We focus on public announcements, which are the simplest epistemic actions, and hence on Public Announcement Logic without the common knowledge operator. As is well known, the epistemic action of publicly announcing a given proposition is semantically represented as a transformation of the model encoding the current epistemic setup of the given agents; the given current model being replaced with its submodel relativized to the (...) announced proposition. We dually characterize the associated submodel-injection map as a certain pseudo-quotient map between the complex algebras respectively associated with the given model and with its relativized submodel. As is well known, these complex algebras are complete atomic BAOs . The dual characterization we provide naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras . Thanks to this construction, the benefits and the wider scope of applications given by a point-free, intuitionistic theory of epistemic updates are made available. As an application of this dual characterization, we axiomatize the intuitionistic analogue of PAL, which we refer to as IPAL, prove soundness and completeness of IPAL w.r.t. both algebraic and relational models, and show that the well known Muddy Children Puzzle can be formalized in IPAL. (shrink)

A finitely alternative normal tense logic \ is a normal tense logic characterized by frames in which every point has at most n future alternatives and m past alternatives. The structure of the lattice \\) is described. There are \ logics in \\) without the finite model property, and only one pretabular logic in \\). There are \ logics in \\) which are not finitely axiomatizable. For \, there are \ logics in \\) without the FMP, and infinitely many pretabular (...) extensions of \. (shrink)

Intuitionistic propositional logic with Galois negations ( \(\mathsf {IGN}\) ) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair \((\lnot,{\sim })\) and dual Galois pair \((\dot{\lnot },\dot{\sim })\) of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for \(\mathsf {IGN}\) are developed. A Hilbert-style axiomatic system \(\mathsf {HN}\) is given for \(\mathsf {IGN}\), and Galois negation logics are defined as extensions of \(\mathsf {IGN}\). We give the bi-tense (...) logic \(\mathsf {S4N}_t\) which is obtained from the minimal tense extension of the modal logic \(\mathsf {S4}\) by adding tense operators. We give a new extended Gödel translation \(\tau \) and prove that \(\mathsf {IGN}\) is embedded into \(\mathsf {S4N}_t\) by \(\tau \). Moreover, every Kripke-complete Galois negation logic _L_ is embedded into its tense companion \(\tau (L)\). (shrink)

A cut-free Gentzen sequent calculus for Ewald’s intuitionistic tense logic \ is established. By the proof-theoretic method, we prove that, for every set of strictly positive implications S, the classical tense logic \ is embedded into its intuitionistic analogue \ via Kolmogorov, Gödel–Genzten and Kuroda translations respectively. A sufficient and necessary condition for Glivenko type theorem in tense logics is established.

Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence (...) relation. The two are the cornerstones of modern logic and have played a crucial role in its development. From the wider perspective, Peirce is led to these theories by three important generalizations: propositions to all signs, truth to scriptibility, and derivation to transformability. We provide an exposition of such proposed semiotic foundation for logical constants and point out a couple of further innovations in this rare text, including the sheet of assertion, correction as a dual of deduction and the nature of conditionals as variably strict conditionals. (shrink)

Peirce introduced Existential Graphs in late 1896, and they were systematically investigated in his 1903 Lowell Lectures. Alpha graphs for classical propositional logic constitute the first part of EGs. The second and the third parts are the beta graphs for first-order logic and the gamma graphs for modal and higher-order logics, among others. As a logical syntax, EGs are two-dimensional graphs, or diagrams, in contrast to the linear algebraic notations. Peirce's theory of EGs is not only a theory of logical (...) syntax but also a proof theory for many logics. A set of transformation rules of graphs defines a proof system for a graphical logic. In this... (shrink)

The language of Belnap–Dunn modal logic \ expands the language of Belnap–Dunn four-valued logic with the modal operator \. We introduce the polarity semantics for \ and its two expansions \ and \ with value operators. The local finitary consequence relation \ in the language \ with respect to the class of all frames is axiomatized by a sequent system \ where \. We prove by using translations between sequents and formulas that these languages under the polarity semantics have the (...) same expressive power on the level of frames with the language \ under the relational semantics for classical modal logic. (shrink)

Intuitionistic modal logics are extensions of intuitionistic propositional logic with modal axioms. We treat with two modal languages ${\mathscr{L}}_\Diamond $ and $\mathscr{L}_{\Diamond,\Box }$ which extend the intuitionistic propositional language with $\Diamond $ and $\Diamond,\Box $, respectively. Gentzen sequent calculi are established for several intuitionistic modal logics. In particular, we introduce a Gentzen sequent calculus for the well-known intuitionistic modal logic $\textsf{MIPC}$. These sequent calculi admit cut elimination and subformula property. They are decidable.

Graded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics.

Labelled tableau systems are developed for subintuitionistic logics \, \ and \. These subintuitionistic logics are embedded into corresponding normal modal logics. Hintikka’s model systems are applied to prove the completeness of labelled tableau systems. The finite model property, decidability and disjunction property are obtained by labelled tableau method.

In recent years, foreign language learning has been proposed as a possible cognitive intervention for older adults. However, the brain network and cognitive functions underlying FLL has remained largely unconfirmed in older adults. In particular, older and younger adults have markedly different cognitive profile—while older adults tend to exhibit decline in most cognitive domains, their semantic memory usually remains intact. As such, older adults may engage the semantic functions to a larger extent than the other cognitive functions traditionally considered the (...) most important. Using anatomical measurements and a cognitive test battery, the present study examined this hypothesis in twenty cognitively normal older adults, who participated in a two-month Italian learning programme. Results showed that the immediate learning success and long-term retention of Italian vocabularies were most consistently predicted by the anatomical measures of the left pars orbitalis and left caudal middle frontal cortex, which are implicated in semantic and episodic memory functions. Convergent evidence was also found based on the pattern of cognitive associations. Our results are consistent with a prominent role of semantic and episodic memory functions in vocabulary learning in older learners. (shrink)

A sequent calculus S for the variety tqBa of all topological quasi-Boolean algebras is established. Using a construction of syntactic finite algebraic model, the finite model property of S is shown, and thus the decidability of S is obtained. We also introduce two non-distributive variants of topological quasi-Boolean algebras. For the variety TDM5 of all topological De Morgan lattices with the axiom 5, we establish a sequent calculus S5 and prove that the cut elimination holds for it. Consequently the decidability (...) of S5 is established. Furthermore, this proof-theoretic method is applied to some subvarieties of TDM5. (shrink)

A contraction-free and cut-free sequent calculus \ for semi-De Morgan algebras, and a structural-rule-free and single-succedent sequent calculus \ for De Morgan algebras are developed. The cut rule is admissible in both sequent calculi. Both calculi enjoy the decidability and Craig interpolation. The sequent calculi are applied to prove some embedding theorems: \ is embedded into \ via Gödel–Gentzen translation. \ is embedded into a sequent calculus for classical propositional logic. \ is embedded into the sequent calculus \ for intuitionistic (...) propositional logic. (shrink)

Purpose – To review and discuss Luciano Floridi’s 2019 book The Logic of Information: A Theory of Philosophy as Conceptual Design, the latest instalment in his philosophy of information (PI) tetralogy, particularly with respect to its implications for library and information studies (LIS). Design/methodology/approach – Nine scholars with research interests in philosophy and LIS read and responded to the book, raising critical and heuristic questions in the spirit of scholarly dialogue. Floridi responded to these questions. Findings – Floridi’s PI, including (...) this latest publication, is of interest to LIS scholars, and much insight can be gained by exploring this connection. It seems also that LIS has the potential to contribute to PI’s further development in some respects. Research implications – Floridi’s PI work is technical philosophy for which many LIS scholars do not have the training or patience to engage with, yet doing so is rewarding. This suggests a role for translational work between philosophy and LIS. Originality/value – The book symposium format, not yet seen in LIS, provides forum for sustained, multifaceted and generative dialogue around ideas. (shrink)

Reading presents an unsolved difficulty for children with hearing loss and research on factors influencing their literacy development is very limited. This work aimed to study the influence of home literacy environment on literacy development of children with hearing loss and explore possible mediating effects of reading interest and parent-child relationship. 112 Chinese children with hearing loss were surveyed for scales of HLE, literacy development, reading interest, and parent-child relationship. Result analysis showed that HLE significantly predicted literacy development of children (...) with hearing loss and this effect was no longer significant after including reading interest and parent-child relationship as variables. Further, HLE significantly predicted reading interest and parent-child relationship, each of which predicted literacy development and played a significant mediating role in HLE’s influence on literacy development. These findings provide educational tips for families of children with hearing loss. (shrink)

Based on sensory integration theory, six fabric samples containing tactile and visual stimuli were selected using the sensory perceptions of designers and combined with balls. Experiments involving these toys were implemented with 15 families with preschool-aged high-functioning autistic children. The results showed that loose sequin , which possessed equal tactile and visual intensities, was strongly correlated with frequent smiling/laughing and high enjoyment levels. The fabric provided a loose tactile sensation regarding surface interweave uniformity and a bright visual sensation regarding visually (...) perceived luster; suede exhibited a greater tactile intensity than visual intensity and was correlated with eye contact and activity response. This fabric possessed a smooth visual sensation regarding visually perceived smoothness; and loose sequin , which possessed equal tactile and visual intensities, was highly correlated with finger pointing and initiation. This fabric offered a thin tactile sensation regarding surface interweave thickness and a bright visual sensation regarding visually perceived luster. We suggest applying fabrics to composite toys. Specifically, loose sequin can be used initially to encourage autistic children to interact; subsequently, suede can enable sustained parent-child interaction. The experimental results provide a reference for establishing an innovative toy-design method for autistic children. Keywords: autism; sensory integration theory; parent-child interaction; toys. (shrink)

Based on sensory integration theory, six fabric samples containing tactile and visual stimuli were selected using the sensory perceptions of designers and combined with balls. Experiments involving these toys were implemented with 15 families with preschool-aged high-functioning autistic children. The results showed that loose sequin, which possessed equal tactile and visual intensities, was strongly correlated with frequent smiling/laughing and high enjoyment levels. The fabric provided a loose tactile sensation regarding surface interweave uniformity and a bright visual sensation regarding visually perceived (...) luster; suede exhibited a greater tactile intensity than visual intensity and was correlated with eye contact and activity response. This fabric possessed a smooth visual sensation regarding visually perceived smoothness; and loose sequin, which possessed equal tactile and visual intensities, was highly correlated with finger pointing and initiation. This fabric offered a thin tactile sensation regarding surface interweave thickness and a bright visual sensation regarding visually perceived luster. We suggest applying fabrics to composite toys. Specifically, loose sequin can be used initially to encourage autistic children to interact; subsequently, suede can enable sustained parent-child interaction. The experimental results provide a reference for establishing an innovative toy-design method for autistic children. Keywords: autism; sensory integration theory; parent-child interaction; toys. (shrink)

Epistemic monadic Boolean algebras are obtained by enriching monadic Boolean algebras with a knowledge operator. Epistemic monadic logic as the monadic fragment of first-order epistemic logic is introduced for talking about knowing things. A Halmos-style representation of epistemic monadic Boolean algebras is established. Relativizations of epistemic monadic algebras are given for modelling updates. These logics are semantically complete.

The finite model property (FMP) in weakly transitive tense logics is explored. Let \(\mathbb {S}=[\textsf{wK}_t\textsf{4}, \textsf{K}_t\textsf{4}]\) be the interval of tense logics between \(\textsf{wK}_t\textsf{4}\) and \(\textsf{K}_t\textsf{4}\). We introduce the modal formula \(\textrm{t}_0^n\) for each \(n\ge 1\). Within the class of all weakly transitive frames, \(\textrm{t}_0^n\) defines the class of all frames in which every cluster has at most _n_ irreflexive points. For each \(n\ge 1\), we define the interval \(\mathbb {S}_n=[\textsf{wK}_t\textsf{4T}_0^{n+1}, \textsf{wK}_t\textsf{4T}_0^{n}]\) which is a subset of \(\mathbb {S}\). There are (...) \(2^{\aleph _0}\) logics in \(\mathbb {S}_n\) lacking the FMP, and there are \(2^{\aleph _0}\) logics in \(\mathbb {S}_n\) having the FMP. Then we explore the FMP in finitely alternative tense logics \(L_{n,m}=L\oplus \{\textrm{Alt}_n^F, \textrm{Alt}_m^P\}\) with \(n,m\ge 0\) and \(L\in \mathbb {S}\). For all \(k\ge 0\) and \(n,m\ge 1\), we define intervals \(\mathbb {F}^k_{n,m}\), \(\mathbb {P}^k_{n,m}\) and \(\mathbb {S}^k_{n,m}\) of tense logics. The number of logics lacking the FMP in them is either 0 or \(2^{\aleph _0}\), and the number of logics having the FMP in them is either finite or \(2^{\aleph _0}\). (shrink)

This work is developed to improve the current quality of e-commerce logistics services. From the perspective of multiple consumer psychology, based on e-commerce, consumer psychology, and other related theories, vegetable e-commerce B is selected as the research object. The commodity quality, accuracy, and timeliness of commodity distribution and other factors of e-commerce B are discussed through questionnaire survey. Then, according to customers’ opinions about “e-commerce B’s distribution and professional aspects that need to be improved,” the research is conducted. Finally, the (...) direction of follow-up optimization is proposed from four different perspectives of multiple consumption psychology. The research results show that more than 89% of the surveyed customers believe that e-commerce B does a good job in terms of commodity quality, accuracy, and timeliness of commodity distribution, and has a high level of logistics service. However, 26.34% of customers hope that e-commerce B can strengthen the protection of personal privacy, 24.97% hope that the platform can add “delay insurance” for goods, and 39.54% hope that the logistics information of purchased goods can be updated in real time. Therefore, e-commerce B needs to be optimized and improved continuously in the future development. Therefore, research on the optimization of logistics service quality of e-commerce is performed under multiple consumption psychology, which provides certain help for the rapid development of subsequent e-commerce. (shrink)

Chinese characters are central to understanding how learners learn to read a logographic script. However, researchers know little about the role of character writing in reading Chinese as a second language. Unlike an alphabetic script, a Chinese character symbol transmits semantic information and is a cultural icon bridging embodied experience and text meaning. As a unique embodied practice, writing by hand contributes to cognitive processing in Chinese reading. Therefore, it is essential to clarify how Chinese character writing, language distance, and (...) cultural background influence CSL reading proficiency. Based on extant research on L2 reading acquisition and strength of key theoretical perspectives of embodied cognition theory, this study tested a regression model for CSL reading involving individual-level factors and group-level predictors. This study collected big data in a sample of 74,362 CSL learners with 67 diverse L1s. Results of hierarchical linear modeling showed a significant effect of CCWP and significant language distance × CCWP interaction effect on reading proficiency; however, cultural background × CCWP interaction effect was not significant. These results conform to the ECT and indicate that bodily activity, past language usage, and cultural background aided reading. CCWP may benefit from withstanding the negative transfer from L1s. Furthermore, CCWP and cultural background are not synergistic predictors of reading. This study may open novel avenues for explorations of CSL reading development. (shrink)

A new characterization of tabularity in tense logic is established, namely, a tense logicLis tabular if and only if$\mathsf {tab}_n^T\in L$for some$n\geq 1$. Two characterization theorems for the Post-completeness in tabular tense logics are given. Furthermore, a characterization of the Post-completeness in the lattice of all tense logics is established. Post numbers of some tense logics are shown.

This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to (...) game theory and business science. This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen University Institute of Logic and Cognition in Guangzhou, China in December 2016. The conference series started in 2001, and is organized by the ILC, often in collaboration with various international research groups. This eighth installment was jointly organized by ILC and Alessandra Palmigiano's Applied Logic research group. The conference series aims to foster the development of effective logical tools to study social behavior from a philosophical, cognitive and formal perspective in order to challenge the field of logic in ways that open up new and exciting research directions. Chapter "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms" of this book is available open access under a CC BY 4.0 license at link.springer.com. (shrink)

A toy is a valuable medium for promoting parent-child interaction. This study selected six light-emitting or reflective materials to produce composite toy balls, and conducted tests on 15 families with preschool-aged high-functioning autistic children. Quantification method I analysis was employed in the study, and the experimental results indicated that the metal ball was the representative sample that elicited many smiles or laughs and much finger pointing as well as high levels of pleasure and activeness.; the mitball was the representative sample (...) that provoked much eye contact, produced satisfactory reactions to activities,; the quality of fluorescence enhanced the levels of pleasure and the reactions to the activity. We propose that dynamic and reflective materials can be adopted to divert the attention of children, and fluorescent toys can then employed to sustain parent-child interaction. (shrink)

We develop a paraconsistent logic by introducing new models for conditionals with acceptive and rejective selection functions which are variants of Chellas’ conditional models. The acceptance and rejection conditions are substituted for truth conditions of conditionals. The paraconsistent conditional logic is axiomatized by a sequent system \ which is an extension of the Belnap-Dunn four-valued logic with a conditional operator. Some acceptive extensions of \ are shown to be sound and complete. We also show the finite acceptive model property and (...) decidability of these logics. (shrink)

Kripke’s Fregean quantification logic FQ fails to formalize the usual first-order logic with identity due to the interpretation of the conditional operator. Motivated by Kripke’s syntax and semantics, the three-valued Fregean quantification logic FQ3 is proposed. This three valued logic differs from Kleene and Łukasiewicz’s three-valued logics. The logic FQ3 is decidable. A sound and complete Hilbert-style axiomatic system for the logic FQ3 is presented.

IntroductionTranscranial direct current stimulation is a noninvasive brain stimulation technique that applied to modulate brain activity and enhance motor recovery. However, the neurobiological substrates underlying the effects of tDCS on brain function remain poorly understood. This study aimed to investigate the central mechanisms of tDCS on improving the athletic performance of male rowing athletes.MethodsTwelve right-handed male professional rowing athletes received tDCS over the left primary motor cortex while undergoing regular training. The resting-state functional magnetic resonance imaging data were acquired before (...) and after tDCS. Measures of amplitude of low-frequency fluctuation and regional homogeneity were calculated and compared between baseline and follow-up, as well as topological measures including global and local efficiency of functional brain networks constructed by graph theoretical analysis.ResultsMale rowing athletes showed increased isokinetic muscle strength of the left knee and left shoulder after tDCS. Increased ALFF values were found in the right precentral gyrus of male rowing athletes after tDCS when compared with those before tDCS. In addition, male rowing athletes showed increased ReHo values in the left paracentral lobule following tDCS. Moreover, increased nodal global efficiency was identified in the left inferior frontal gyrus of male rowing athletes after tDCS.ConclusionThe findings suggested that simultaneous tDCS-induced excitation over the primary motor cortex might potentially improve the overall athletic performance in male rowing athletes through the right precentral gyrus and left paracentral lobule, as well as left inferior frontal gyrus. (shrink)

Quasi-Boolean modal algebras are quasi-Boolean algebras with a modal operator satisfying the interaction axiom. Sequential quasi-Boolean modal logics and the relational semantics are introduced. Kripke-completeness for some quasi-Boolean modal logics is shown by the canonical model method. We show that every descriptive persistent quasi-Boolean modal logic is canonical. The finite model property of some quasi-Boolean modal logics is proved. A cut-free Gentzen sequent calculus for the minimal quasi-Boolean logic is developed and we show that it has the Craig interpolation property.

Mandalas in the Making: The Visual Culture of Esoteric Buddhism at Dunhuang, by Michelle C. Wang. Leiden: Brill, 2018. xviii + 318 pages. Hb. $147.00, ISBN-13: 9789004357655; Ebook $25.00, ISBN-13: 9789004360402.

The global consequence relation of a normal modal logic \ is formulated as a global sequent calculus which extends the local sequent theory of \ with global sequent rules. All global sequent calculi of normal modal logics admits global cut elimination. This property is utilized to show that decidability is preserved from the local to global sequent theories of any normal modal logic over \. The preservation of Craig interpolation property from local to global sequent theories of any normal modal (...) logic is shown by proof-theoretic method. (shrink)

Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus, many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate modal logics of all cardinalities. Thus ways of exploring model-theoretic logics (...) can be transferred to modal logics. (shrink)

This paper concentrates on the event-triggered H ∞ filter design for the discrete-time Markovian jump neural networks under random missing measurements and cyber attacks. Considering that the controlled system and the filtering can exchange information over a shared communication network which is vulnerable to the cyber attacks and has limited bandwidth, the event-triggered mechanism is proposed to relieve the communication burden of data transmission. A variable conforming to Bernoulli distribution is exploited to describe the stochastic phenomenon since the missing measurements (...) occur with random probability. Furthermore, seeing that the communication networks are vulnerable to external malicious attacks, the transferred information via the shared communication network may be changed by the injected false information from the attackers. Based on the above consideration, sufficient conditions for the filtering error system to maintain asymptotically stable are provided with predefined H ∞ performance. In the end, three numerical examples are given to verify the proposed theoretical results. (shrink)