Kripke completeness of some infinitary predicate modal logics is presented. More precisely, we prove that if a normal modal logic above is -persistent and universal, the infinitary and predicate extension of with BF and BF is Kripke complete, where BF and BF denote the formulas pi pi and x x, respectively. The results include the completeness of extensions of standard modal logics such as , and its extensions by the schemata T, B, 4, 5, D, and their combinations. The proof (...) is obtained by extending the correspondence between the representation of modal algebras and the completeness of propositional modal logic to infinite. (shrink)

Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same (...) consequence relations for a given spi-logic. (shrink)

In this paper, we discuss semantical properties of the logic \(\textbf{GL}\) of provability. The logic \(\textbf{GL}\) is a normal modal logic which is axiomatized by the the Löb formula \( \Box (\Box p\supset p)\supset \Box p \), but it is known that \(\textbf{GL}\) can also be axiomatized by an axiom \(\Box p\supset \Box \Box p\) and an \(\omega \) -rule \((\Diamond ^{*})\) which takes countably many premises \(\phi \supset \Diamond ^{n}\top \) \((n\in \omega )\) and returns a conclusion \(\phi \supset (...) \bot \). We show that the class of transitive Kripke frames which validates \((\Diamond ^{*})\) and the class of transitive Kripke frames which strongly validates \((\Diamond ^{*})\) are equal, and that the following three classes of transitive Kripke frames, the class which validates \((\Diamond ^{*})\), the class which weakly validates \((\Diamond ^{*})\), and the class which is defined by the Löb formula, are mutually different, while all of them characterize \(\textbf{GL}\). This gives an example of a proof system _P_ and a class _C_ of Kripke frames such that _P_ is sound and complete with respect to _C_ but the soundness cannot be proved by simple induction on the height of the derivations in _P_. We also show Kripke completeness of the proof system with \((\Diamond ^{*})\) in an algebraic manner. As a corollary, we show that the class of modal algebras which is defined by equations \(\Box x\le \Box \Box x\) and \(\bigwedge _{n\in \omega }\Diamond ^{n}1=0\) is not a variety. (shrink)

Predicate modal logics based on Kwith non-compact extra axioms are discussed and a sufficient condition for the model existence theorem is presented. We deal with various axioms in a general way by an algebraic method, instead of discussing concrete non-compact axioms one by one.

We give an extension of the Jónsson‐Tarski representation theorem for both normal and non‐normal modal algebras so that it preserves countably many infinite meets and joins. In order to extend the Jónsson‐Tarski representation to non‐normal modal algebras we consider neighborhood frames instead of Kripke frames just as Došen's duality theorem for modal algebras, and to deal with infinite meets and joins, we make use of Q‐filters, which were introduced by Rasiowa and Sikorski, instead of prime filters. By means of the (...) extended representation theorem, we show that every predicate modal logic, whether it is normal or non‐normal, has a model defined on a neighborhood frame with constant domains, and we give a completeness theorem for some predicate modal logics with respect to classes of neighborhood frames with constant domains. Similarly, we show a model existence theorem and a completeness theorem for infinitary modal logics which allow conjunctions of countably many formulas. (shrink)

It is known that for any subdirectly irreducible finite Heyting algebra A and any Heyting algebra B, A is embeddable into a quotient algebra of B, if and only if Jankov’s formula χ A for A is refuted in B. In this paper, we present an infinitary extension of the above theorem given by Jankov. More precisely, for any cardinal number κ, we present Jankov’s theorem for homomorphisms preserving infinite meets and joins, a class of subdirectly irreducible complete κ-Heyting algebras (...) and κ-infinitary logic, where a κ-Heyting algebra is a Heyting algebra A with # ≥ κ and κ-infinitary logic is the infinitary logic such that for any set Θ of formulas with # Θ ≥ κ, ∨Θ and ∧Θ are well defined formulas. (shrink)

It is known that for any subdirectly irreducible finite Heyting algebra A and any Heyting algebra, B, A is embeddable into a quotient algebra of B, if and only if Jankov's formula ${\rm{\chi A}}$ A for A is refuted in B. In this paper, we present an infinitary extension of the above theorem given by Jankov. More precisely, for any cardinal number ${\rm{\kappa }}$, we present Jankov's theorem for homomorphisms preserving infinite meets and joins, a class of subdirectly irreducible complete (...) ${\rm{\kappa }}$ - Heyting algebras and ${\rm{\kappa }}$ - infinitary logic, where a ${\rm{\kappa }}$ -Heyting algebra is a Heyting algebra A with ${\rm{\# A}} \le {\rm{\kappa }}$ and ${\rm{\kappa }}$ - infinitary logic is the infinitary logic such that for any set ${\rm{\Theta }}$ of formulas with ${\rm{\# \Theta }} \le {\rm{\kappa }}$ ⌈ Θ and ‷ Θ are well defined formulas. (shrink)

In this article, a cut-free system TLMω1 for infinitary propositional modal logic is proposed which is complete with respect to the class of all Kripke frames.The system TLMω1 is a kind of Gentzen style sequent calculus, but a sequent of TLMω1 is defined as a finite tree of sequents in a standard sense. We prove the cut-elimination theorem for TLMω1 via its Kripke completeness.

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter (...) showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole. (shrink)

あはれ・わび・いきなどの美意識や芸術の本質について、和辻哲郎、九鬼周造などの知の巨人から学ぶ。.

In this paper, using Mark Schroeder’s (2008a) expressivist semantic framework for normative language as a case study, I will identify difficulties that even an expressivist semantic theory capable of addressing the Frege-Geach problem will encounter in handling the logical possibility of moral dilemmas. To this end, I will draw on a classical puzzle formulated by McConnell (1978) that the logical possibility of moral dilemmas conflicts with some of the prima facie plausible axioms of the standard deontic logic, which include obligation (...) implies permission. On the tentative assumption that proponents of ethical expressivism should be generally committed to securing the logical possibility of moral dilemmas in their semantic theories, I will explore whether and how expressivists can successfully invalidate obligation implies permission within the framework developed by Schroeder. The case study eventually reveals that this can indeed be a hard task for expressivists. Generalizing from the case study, I will suggest that the source of the difficulty ultimately lies in the mentalist assumption of the expressivist semantic project that the logico-semantic relations exhibited by normative sentences should be modeled in terms of the psychological attitudes that speakers express by uttering them. My final goal will be to show that the difficulty expressivists face in dealing with the logical possibility of moral dilemmas is a reflection of the more general problem that their commitment to the mentalist assumption prevents them from flexibly adopting or dropping axioms in their semantic theories to get the right technical results. (shrink)

U ovom radu, koristeći Mark Schroederov (2008a) semantički okvir za ekspresivistički normativni jezik kao studiju slučaja, identificirat ću poteškoće s kojima će se čak i ekspresivistička semantička teorija sposobna za rješavanje Frege-Geach problema susresti pri objašnjenju logičke mogućnosti moralnih dilema. U tu svrhu, oslonit ću se na klasičnu zagonetku koju je formulirao McConnell (1978)a pokazuje da se logička mogućnost moralnih dilema sukobljava s nekim od naizgled opravdanih aksioma standardne deontičke logike, među kojima je i aksiom da obaveza implicira dopuštenost. Na (...) temelju tentativne pretpostavke da zastupnici etičkog ekspresivizma trebaju općenito biti posvećeni osiguravanju logičke mogućnosti moralnih dilema u svojim semantičkim teorijama, istražit ću da li i kako ekspresivisti mogu uspješno opovrgnuti aksiom da obaveza implicira dopuštenje unutar okvira koji je razvio Schroeder. Studija slučaja konačno otkriva da to može biti zaista težak zadatak za ekspresiviste. Generalizirajući iz studije slučaja, sugerirat ću da izvor poteškoće leži u mentalističkoj pretpostavci ekspresivističkog semantičkog projekta da bi logičko-semantički odnosi prikazani normativnim rečenicama trebali biti modelirani pomoću psiholoških stavova koje govornici izražavaju izgovarajući ih. Moj konačni cilj će biti pokazati da je poteškoća s kojom se ekspresivisti susreću u suočavanju s logičkom mogućnosti moralnih dilema odraz općeg problema da njihova predanost mentalističkoj pretpostavci sprječava fleksibilno usvajanje ili odbacivanje aksioma u njihovim semantičkim teorijama kako bi dobili ispravne tehničke rezultate. (shrink)

My life as a quantum physicist / M. Nakahara -- A review on operator quantum error correction - Dedicated to Professor Mikio Nakahara on the occasion of his 60th birthday / C.-K. Li, Y.-T. Poon and N.-S. Sze -- Implementing measurement operators in linear optical and solid-state qubits / Y. Ota, S. Ashhab and F. Nori -- Fast and accurate simulation of quantum computing by multi-precision MPS: Recent development / A. Saitoh -- Entanglement properties of a quantum lattice-gas model on (...) square and triangular ladders / S. Tanaka, R. Tamura and H. Katsura -- On signal amplification from weak-value amplification / Y. Shikano -- Topological protection of quantum information / K. Fujii -- Quantum annealing with antiferromagnetic fluctuations for mean-field models / Y. Seki and H. Nishimori -- A method to change phase transition nature - Toward annealing methods / R. Tamura and S. Tanaka -- Computational analysis of the first stage of the photosynthetic system, the light-dependent reaction, by quantum chemical simulation method / M. Tada-Umezaki -- Two-qubit gate operation on selected nearest neighboring qubits in a neutral atom quantum computer / E. Hosseini Lapasar... [et al.] -- A simple operator quantum error correction scheme avoiding fully correlated errors / C. Bagnasco, Y. Kondo and M. Nakahara -- Black hole predictability, classical and quantum / A. Ishibashi -- Classical field simulation of finite-temperature Bose gases / T. Sato -- Atomic quantum simulations of lattice gauge theory: Effect of gauge symmetry breaking / K. Kasamatsu, I. Ichinose and T. Matsui -- Recursive construction of noiseless subsystem for qudits / U. Gungordu... [et al.] -- Composite quantum gates for precise quantum control / M. Bando... [et al.] -- New formulation of statistical mechanics using thermal pure quantum states / S. Sugiura and A. Shimizu -- Thermodynamics in unitary time evolution / T. N. Ikeda -- Second law of thermodynamics with QC-mutual information / T. Sagawa. (shrink)

Possible worlds have revolutionised philosophy and some related fields. But, in recent years, tools based on possible worlds have been found to be limited in many respects. Impossible worlds have been introduced to overcome these limitations. This Element aims to raise and answer the neglected question of what is characteristically impossible about impossible worlds. The Element sheds new light on the nature of impossible worlds. It also aims to analyse the main features and utility of impossible worlds and examine how (...) impossible worlds can capture distinctions which are unavailable if we limit ourselves to possible world-based tools. (shrink)

丸山眞男は西洋近代至上主義者・国民国家至上主義者だったのか。丸山が「主体性」論で追究しようとしていたものは何か。著作、講義録をいま一度丁寧に読みなおし、「他者感覚」「自己内対話」など新たな視点から、誤 解されがちな丸山思想の可能性を探る。.

新しい社会科学の構築へ。来たるべき社会の基礎となる社会科学的方法論の課題を、第一線で活躍する十二名が「思想学」の観点から論じる。自由思想、啓蒙思想から神学、経済学まで多彩な視座より先哲の歩みを分析し、 思想研究の未来を探る充実の書。.

世界に溢れ続けるイメージは喫緊の思想的・文化的テーマである。像=イメージを行為主体と捉えるブレーデカンプによる像行為論の可能性を検討しつつ、独自の「像即是空、空即是像」たる「かげ」としての論理へと至る 最新論集。.

三島由紀夫、江藤淳、西部邁...戦後日本の保守論客たちの自死は何を意味するのか?「近代」思想が破壊しようとする、伝統文化と秩序。その背景にあるユダヤ思想の正体、そしてマルクス主義との関連を明らかにする 。日本人の劣化・自滅は防げるか?

This book enables readers to understand contemporary Japanese society and culture. Since it is written by experts, it allows readers to start with any chapters they are interested in. It also provides a unique way to introduce Japanese society and culture to those who have never visited or studied Japanese society by reading articles from various authors on topics such as gender, family, economy, natural disasters and politics and laws. It provides scholars, academics, graduate students and the general educated audience (...) all the information required to understand contemporary Japanese society and culture fully and see the diverse perspectives available. (shrink)

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel (...) way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic. (shrink)

We prove that every countable non-standard model of WKL0 has a proper initial part isomorphic to itself. This theorem enables us to carry out non-standard arguments over WKL0.

Although numerous disciplines recognize multiple ways of conceptualizing time, Stefan Tanaka argues that scholars still overwhelmingly operate on chronological and linear Newtonian or classical time that emerged during the Enlightenment. This short, approachable book implores the humanities and humanistic social sciences to actively embrace the richness of different times that are evident in non-modern societies and have become common in several scientific fields throughout the twentieth century. Tanaka first offers a history of chronology by showing how the social (...) structures built on clocks and calendars gained material expression. Tanaka then proposes that we can move away from this chronology by considering how contemporary scientific understandings of time might be adapted to reconceive the present and pasts. This opens up a conversation that allows for the possibility of other ways to know about and re-present pasts. A multiplicity of times will help us broaden the historical horizon by embracing the heterogeneity of our lives and world via rethinking the complex interaction between stability, repetition, and change. This history without chronology also allows for incorporating the affordances of digital media. (shrink)

An assessment of mood or emotion is important in developing mental health measures, and facial expressions are strongly related to mood or emotion. This study thus aimed to examine the relationship between levels of negative mood and characteristics of mouth parts when moods are drawn as facial expressions on a common platform. A cross-sectional study of Japanese college freshmen was conducted, and 1,068 valid responses were analyzed. The questionnaire survey consisted of participants’ characteristics, the Profile of Mood States, and a (...) sheet of facial expression drawing, and the sheet was digitized and analyzed using an image-analysis software. Based on the total POMS score as an index of negative mood, the participants were divided into four groups: low, normal, high, and very high. Lengths of drawn lines and between both mouth corners were significantly longer, and circularity and roundness were significantly higher in the L group. With increasing levels of negative mood, significant decreasing trends were observed in these lengths. Convex downward and enclosed figures were significantly predominant in the L group, while convex upward figures were significantly predominant and a tendency toward predominance of no drawn mouths or line figures was found in the H and VH groups. Our results suggest that mood states can be significantly related to the size and figure characteristics of drawn mouths of FACED on a non-verbal common platform. That is, these findings mean that subjects with low negative mood may draw a greater and rounder mouth and figures that may be enclosed and downward convex, while subjects with a high negative mood may not draw the line, or if any, may draw the line shorter and upward convex. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)