The laser chaos decision maker has been demonstrated to enable ultra-high-speed solutions of multiarmed bandit problems or decision-making in the GHz order. However, the underlying mechanisms are not well understood. In this paper, we analyze the chaotic dynamics inherent in experimentally observed laser chaos time series via surrogate data and further accelerate the decision-making performance via parameter optimization. We first evaluate the negative autocorrelation in a chaotic time series and its impact on decision-making detail. Then, we analyze the decision-making ability (...) using three different surrogate chaos time series to examine the underlying mechanism. We clarify that the negative autocorrelation of laser chaos improves decision-making and that the amplitude distribution of the original laser chaos time series is not optimal. Hence, we introduce a new parameter for adjusting the amplitude distribution of the laser chaos to enhance the decision-making performance. This study provides a new insight into exploiting the supremacy of chaotic dynamics in artificially constructed intelligent systems. (shrink)

Short interspersed repetitive elements, or SINEs, are tRNA-derived retroposons that are dispersed throughout eukaryotic genomes and can be present in well over 104 total copies. The enormous volume of SINE amplifications per organism makes them important evolutionary agents for shaping the diversity of genomes, and the irreversible, independent nature of their insertion allows them to be used for diagnosing common ancestry among host taxa with extreme confidence. As such, they represent a powerful new tool for systematic biology that can be (...) strategically integrated with other conventional phylogenetic characters, most notably morphology and DNA sequences. This review covers the basic aspects of SINE evolution that are especially relevant to their use as systematic characters and describes the practical methods of characterizing SINEs for cladogram construction. It also discusses the limits of their systematic utility, clarifies some recently published misunderstandings, and illustrates the effective application of SINEs for vertebrate phylogenetics with results from selected case studies. BioEssays 22:148–160, 2000. ©2000 John Wiley & Sons, Inc. (shrink)

We introduce an extended intuitionistic linear logic with strong negation and modality. The logic presented is a modal extension of Wansing's extended linear logic with strong negation. First, we propose three types of cut-free sequent calculi for this new logic. The first one is named a subformula calculus, which yields the subformula property. The second one is termed a dual calculus, which has positive and negative sequents. The third one is called a triple-context calculus, which is regarded as a natural (...) extension or generalization of Hodas and Miller's dual-context calculus appearing in a linear logic programming language. Second, we present a concurrent process calculus based on the logic. This calculus is an extension of Okada's process calculus. Third, we introduce a Kripke type semantics for a fragment of the logic, and show the completeness theorems with respect to the semantics. Finally, we mention a logic programming language based on the triple-context calculus. (shrink)

Illusory kinesthetic sensation was influenced by motor imagery of the wrist following tendon vibration. The imagery and the illusion conditions commonly activated the contralateral cingulate motor area, supplementary motor area, dorsal premotor cortex, and ipsilateral cerebellum. This supports the notion that motor imagery is a mental rehearsal of movement, during which expected kinesthetic sensation is emulated by recruiting multiple motor areas, commonly activated by pure kinesthesia.

There is a task-specificity in the visual-tactile interaction for perception: The polymodal posterior parietal cortex is related to the comparison of the shapes coded by different sensory modalities, whereas the lateral occipital complex is the part of the network for multimodal shape identification. These interactions may be mediated by some latent pathways potentiated by sensory deprivation or learning.

日本の戦後思想の核心とは、圧倒的な外来思想への、自己の戦争体験と近代日本の露わになった後進性を手がかりにした、ポストコロニアルな抵抗にある。非西洋世界が近代化にむけた苦闘にあるこのとき、日本の戦後思想 は、どのような可能性をもつのか。「リスク近代」の果てにせり上がってきた、世界が抱え込む「有限性」という概念を手がかりに、21世紀世界の思想的課題と、未来構想の可能性を問う。.

The paper traces the development and the role of syntactic reduction in Edmund Husserl’s early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” (...) The paper argues that the notion anticipates the notion of reduction in term rewrite theory in computer science. The role of the reduction for Husserl is, however, primarily epistemological: its purpose is to impart clarity to formal mathematics. (shrink)

A new combined temporal logic called synchronized linear-time temporal logic (SLTL) is introduced as a Gentzen-type sequent calculus. SLTL can represent the n -Cartesian product of the set of natural numbers. The cut-elimination and completeness theorems for SLTL are proved. Moreover, a display sequent calculus δ SLTL is defined.

Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is (...) addressed. (shrink)

A modal extension of multilattice logic, called modal multilattice logic, is introduced as a Gentzen-type sequent calculus \. Theorems for embedding \ into a Gentzen-type sequent calculus S4C and vice versa are proved. The cut-elimination theorem for \ is shown. A Kripke semantics for \ is introduced, and the completeness theorem with respect to this semantics is proved. Moreover, the duality principle is proved as a characteristic property of \.

This study introduces refutation-aware Gentzen-style sequent calculi and Kripke-style semantics for propositional until-free linear-time temporal logic. The sequent calculi and semantics are constructed on the basis of the refutation-aware setting for Nelson’s paraconsistent logic. The cut-elimination and completeness theorems for the proposed sequent calculi and semantics are proven.

Advancements in novel neurotechnologies, such as brain computer interfaces and neuromodulatory devices such as deep brain stimulators, will have profound implications for society and human rights. While these technologies are improving the diagnosis and treatment of mental and neurological diseases, they can also alter individual agency and estrange those using neurotechnologies from their sense of self, challenging basic notions of what it means to be human. As an international coalition of interdisciplinary scholars and practitioners, we examine these challenges and make (...) recommendations to mitigate negative consequences that could arise from the unregulated development or application of novel neurotechnologies. We explore potential ethical challenges in four key areas: identity and agency, privacy, bias, and enhancement. To address them, we propose democratic and inclusive summits to establish globally-coordinated ethical and societal guidelines for neurotechnology development and application, new measures, including “Neurorights,” for data privacy, security, and consent to empower neurotechnology users’ control over their data, new methods of identifying and preventing bias, and the adoption of public guidelines for safe and equitable distribution of neurotechnological devices. (shrink)

In this study, falsification-aware semantics and sequent calculi for first-order classical logic are introduced and investigated. These semantics and sequent calculi are constructed based on a falsification-aware setting for first-order Nelson constructive three-valued logic. In fact, these semantics and sequent calculi are regarded as those for a classical variant of N3. The completeness and cut-elimination theorems for the proposed semantics and sequent calculi are proved using Schütte’s method. Similar results for the propositional case are also obtained.

Lattice logic, bilattice logic, and paraconsistent quantum logic are investigated based on monosequent systems. Paraconsistent quantum logic is an extension of lattice logic, and bilattice logic is an extension of paraconsistent quantum logic. Monosequent system is a sequent calculus based on the restricted sequent that contains exactly one formula in both the antecedent and succedent. It is known that a completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic. A completeness theorem with respect (...) to a lattice-valued semantics is proved for paraconsistent quantum logic, and a completeness theorem with respect to a bilattice-valued semantics is proved for bilattice logic. Some syntactical properties, including cut-elimination and duality, are also investigated for the monosequent systems for these logics. (shrink)

A classical paraconsistent logic, which is regarded as a modified extension of first-degree entailment logic, is introduced as a Gentzen-type sequent calculus. This logic can simulate the classical negation in classical logic by paraconsistent double negation in CP. Theorems for syntactically and semantically embedding CP into a Gentzen-type sequent calculus LK for classical logic and vice versa are proved. The cut-elimination and completeness theorems for CP are also shown using these embedding theorems. Similar results are also obtained for an intuitionistic (...) paraconsistent logic, and several versions of Glivenko and Gödel-Gentzen translation theorems are proved for CP and IP. (shrink)

The strong normalization theorem is uniformly proved for typed λ-calculi for a wide range of substructural logics with or without strong negation.

We introduce several restricted versions of the structural rules in the implicational fragment of Gentzen's sequent calculus LJ. For example, we permit the applications of a structural rule only if its principal formula is an implication. We investigate cut-eliminability and theorem-equivalence among various combinations of them. The results include new cut-elimination theorems for the implicational fragments of the following logics: relevant logic E, strict implication S4, and their neighbors (e.g., E-W and S4-W); BCI-logic, BCK-logic, relevant logic R, and the intuitionistic (...) logic. (shrink)

In this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic (...) determined by the algebraic structure of multilattices. Similar completeness and embedding results are also shown for another logic called bi-intuitionistic connexive multilattice logic, obtained by replacing the connectives of intuitionistic implication and co-implication with their connexive variants. (shrink)

Proof-theory has traditionally been developed based on linguistic (symbolic) representations of logical proofs. Recently, however, logical reasoning based on diagrammatic or graphical representations has been investigated by logicians. Euler diagrams were introduced in the eighteenth century. But it is quite recent (more precisely, in the 1990s) that logicians started to study them from a formal logical viewpoint. We propose a novel approach to the formalization of Euler diagrammatic reasoning, in which diagrams are defined not in terms of regions as in (...) the standard approach, but in terms of topological relations between diagrammatic objects. We formalize the unification rule, which plays a central role in Euler diagrammatic reasoning, in a style of natural deduction. We prove the soundness and completeness theorems with respect to a formal set-theoretical semantics. We also investigate structure of diagrammatic proofs and prove a normal form theorem. (shrink)

It is well known that the modal logic S5 can be embedded in the classical predicate logic by interpreting the modal operator in terms of a quantifier. Wajsberg [10] proved this fact in a syntactic way. Mints [7] extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable. In this paper we extend Mints' result to the basic modal logic S4; we (...) investigate the correspondence between the quantified versions of S4 (with and without the Barcan formula) and the classical predicate logic (with one-sorted variable). We present a purely proof-theoretic proof-transformation method, reducing an LK-proof of an interpreted formula to a modal proof. (shrink)

Falsification-aware (hyper)sequent calculi and Kripke semantics for normal modal logics including S4 and S5 are introduced and investigated in this study. These calculi and semantics are constructed based on the idea of a falsification-aware framework for Nelson’s constructive three-valued logic. The cut-elimination and completeness theorems for the proposed calculi and semantics are proved.

In the performing arts, such as music and dance performances, people actively interact with each other and show their exciting performances. Some studies have proposed that this interaction is a social origin of the performing arts. Some have further investigated this phenomenon based on the synchronization and coordination theory. Though the majority of these studies have focused on the collaborative context, several genres of the performing arts, such as jazz sessions and breakdance battles, have a competitive context. Several studies have (...) suggested that, in this competitive context, performers actively interact with each other and construct some correspondence. Moreover, a few recent studies focusing on competitive conversations, such as debates, have shown that, compared to people's interactions in collaborative conversations, people in competitive contexts frequently coordinate their behaviors in complicated ways. However, the interaction and coordination among performers in these competitive contexts have not been sufficiently investigated. Therefore, we investigated the coordination of expert breakdancers in battle scenes and measured their rhythmic movements using a motion capture system. We calculated the relative phase of the rhythmic movements between two dancers to investigate their coordination. The results showed that the dancers' rhythmic movements tended to synchronize in an anti-phase fashion, which means that there were similarities as well as differences between the two dancers' rhythmic movements. Furthermore, this pattern of coordination changed dynamically as time elapsed, from an in-phase synchronization or leader-follower relationships to an anti-phase synchronization and then leader-follower relationships. (shrink)

Two intuitionistic paradefinite logics N4C and N4C+ are introduced as Gentzen-type sequent calculi. These logics are regarded as a combination of Nelson’s paraconsistent four-valued logic N4 and Wansing’s basic constructive connexive logic C. The proposed logics are also regarded as intuitionistic variants of Arieli, Avron, and Zamansky’s ideal paraconistent four-valued logic 4CC. The logic N4C has no quasi-explosion axiom that represents a relationship between conflation and paraconsistent negation, but the logic N4C+ has this axiom. The Kripke-completeness and cut-elimination theorems for (...) N4C and N4C+ are proved. (shrink)

Two new multilattice logics called submultilattice logic and indexed multilattice logic are introduced as a monosequent calculus and an indexed monosequent calculus, respectively. The submultilattice logic is regarded as a monosequent calculus version of Shramko’s original multilattice logic, which is also known as the logic of logical multilattices. The indexed multilattice logic is an extension of the submultilattice logic, and is regarded as the logic of multilattices. A completeness theorem with respect to a lattice-valued semantics is proved for the submultilattice (...) logic, and a completeness theorem with respect to a multilattice-valued semantics is proved for the indexed multilattice logic. (shrink)

In this study, we introduce Gentzen-type sequent calculi BDm and BDi for a modal extension and an intuitionistic modification, respectively, of De and Omori’s extended Belnap–Dunn logic BD+ with classical negation. We prove theorems for syntactically and semantically embedding BDm and BDi into Gentzen-type sequent calculi S4 and LJ for normal modal logic and intuitionistic logic, respectively. The cut-elimination, decidability, and completeness theorems for BDm and BDi are obtained using these embedding theorems. Moreover, we prove the Glivenko theorem for embedding (...) BD+ into BDi and the McKinsey–Tarski theorem for embedding BDi into BDm. (shrink)

The trilattice SIXTEEN3 introduced in Shramko & Wansing (2005) is a natural generalization of the famous bilattice FOUR2. Some Hilbert-style proof systems for trilattice logics related to SIXTEEN3 have recently been studied (Odintsov, 2009; Shramko & Wansing, 2005). In this paper, three sequent calculi GB, FB, and QB are presented for Odintsovs coordinate valuations associated with valuations in SIXTEEN3. The equivalence between GB, FB, and QB, the cut-elimination theorems for these calculi, and the decidability of B are proved. In addition, (...) it is shown how the sequent systems for B can be extended to cut-free sequent calculi for Odintsov’s LB, which is an extension of B by adding classical implication and negation connectives. (shrink)

Gentzen-type sequent calculi GBD+, GBDe, GBD1, and GBD2 are respectively introduced for De and Omori’s axiomatic extensions BD+, BDe, BD1, and BD2 of Belnap–Dunn logic by adding classical negation. These calculi are constructed based on a small modification of the original characteristic axiom scheme for negated implication. Theorems for syntactically and semantically embedding these calculi into a Gentzen-type sequent calculus LK for classical logic are proved. The cut-elimination, decidability, and completeness theorems for these calculi are obtained using these embedding theorems. (...) Similar results excluding cut-elimination results are also obtained for alternative Gentzen-type sequent calculi gBD+, gBDe, gBD1, and gBD2 for BD+, BDe, BD1, and BD2, respectively. These alternative calculi are constructed based on the original characteristic axiom scheme for negated implication. (shrink)

A new logic, quantized intuitionistic linear logic, is introduced, and is closely related to the logic which corresponds to Mulvey and Pelletier's involutive quantales. Some cut-free sequent calculi with a new property quantization principle and some complete semantics such as an involutive quantale model and a quantale model are obtained for QILL. The relationship between QILL and Wansing's extended intuitionistic linear logic with strong negation is also observed using such syntactical and semantical frameworks.

Dual-intuitionistic logics are logics proposed by Czermak , Goodman and Urbas . It is shown in this paper that there is a correspondence between Goodman's dual-intuitionistic logic and Nelson's constructive logic N−.

This study aims to introduce a modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC as a Gentzen-type sequent calculus and prove the Kripke-completeness and cut-elimination theorems for M4CC. The logic M4CC is also shown to be decidable and embeddable into the normal modal logic S4. Furthermore, a subsystem of M4CC, which has some characteristic properties that do not hold for M4CC, is introduced and the Kripke-completeness and cut-elimination theorems for this subsystem are proved. This subsystem (...) is also shown to be decidable and embeddable into S4. (shrink)

Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic (MALL) and for affine logic (LLW), i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL (which we call IMALL), and intuitionistic LLW (which we call ILLW). In addition, we shall show the finite model property for contractive linear logic (LLC), i.e., linear logic with contraction, and for its intuitionistic version (ILLC). (...) The finite model property for related substructural logics also follow by our method. In particular, we shall show that the property holds for all of FL and GL - -systems except FL c and GL - c of Ono [11], that will settle the open problems stated in Ono [12]. (shrink)

It is well known that the modal logic S5 can be embedded in the classical predicate logic by interpreting the modal operator in terms of a quantifier. Wajsberg proved this fact in a syntactic way. Mints extended this result to the quantified version of S5; using a purely proof-theoretic method he showed that the quantified S5 corresponds to the classical predicate logic with one-sorted variable. In this paper we extend Mints’ result to the basic modal logic S4; we investigate the (...) correspondence between the quantified versions of S4 and the classical predicate logic. We present a purely proof-theoretic proof-transformation method, reducing an LK-proof of an interpreted formula to a modal proof. (shrink)

A general Gentzen-style framework for handling both bilattice (or strong) negation and usual negation is introduced based on the characterization of negation by a modal-like operator. This framework is regarded as an extension, generalization or re- finement of not only bilattice logics and logics with strong negation, but also traditional logics including classical logic LK, classical modal logic S4 and classical linear logic CL. Cut-elimination theorems are proved for a variety of proposed sequent calculi including CLS (a conservative extension of (...) CL) and CLScw (a conservative extension of some bilattice logics, LK and S4). Completeness theorems are given for these calculi with respect to phase semantics, for SLK (a conservative extension and fragment of LK and CLScw, respectively) with respect to a classical-like semantics, and for SS4 (a conservative extension and fragment of S4 and CLScw, respectively) with respect to a Kripke-type semantics. The proposed framework allows for an embedding of the proposed calculi into LK, S4 and CL. (shrink)

We introduce Kripke semantics for modal substructural logics, and provethe completeness theorems with respect to the semantics. Thecompleteness theorems are proved using an extended Ishihara's method ofcanonical model construction (Ishihara, 2000). The framework presentedcan deal with a broad range of modal substructural logics, including afragment of modal intuitionistic linear logic, and modal versions ofCorsi's logics, Visser's logic, Méndez's logics and relevant logics.