In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics.

LetL be any modal or tense logic with the finite model property. For eachm, definer L (m) to be the smallest numberr such that for any formulaA withm modal operators,A is provable inL if and only ifA is valid in everyL-model with at mostr worlds. Thus, the functionr L determines the size of refutation Kripke models forL. In this paper, we will give an estimation ofr L (m) for some linear modal and tense logicsL.

This paper discusses Crawley completions of residuated lattices. While MacNeille completions have been studied recently in relation to logic, Crawley completions (i.e. complete ideal completions), which are another kind of regular completions, have not been discussed much in this relation while many important algebraic works on Crawley completions had been done until the end of the 70’s. In this paper, basic algebraic properties of ideal completions and Crawley completions of residuated lattices are studied first in their conncetion with the join (...) infinite distributivity and Heyting implication. Then some results on algebraic completeness and conservativity of Heyting implication in substructural predicate logics are obtained as their consequences. (shrink)

John Henry Newman has rightly been hailed as a giant in the Catholic intellectual tradition. His contributions to theology, literature, and education have been studied at length; however, his contribution to philosophy has not received appropriate attention. This essay 1) explores Newman’s unique philosophical insights in terms of the phenomenological tradition of Edmund Husserl; 2) analyzes the transcendental approach of certain British scientists—notably Ronald Knox and Charles Darwin; and 3) discusses how Newman might be considered a phenomenologist.

Epistemological investigation belonged to the core topics in Indian philosophical traditions, too. Right cognition had generally been regarded as one of the important means to emancipation (niḥśreyasa) since ancient times. To reach this religious goal, they keenly discussed the problems of what kinds of cognition we should accept as right or what kinds of objects a right cognition refers to. Specifically it is about the number and the nature of the means of right cognition that opinions differ from school to (...) school. The number ranges from one (perception) to six or even ten (perception, inference, comparison, testimony, implication, non-perception, equivalence, tradition, gesture, and intuition). The concept of each means of right cognition, too, varies greatly among schools. In this paper I take up the Nyāya System, a rationalistic school of Brahmanic philosophy. In Nyāya the inference is regarded as particularly important, but it never means that logical thinking dominates testimony or the authority of religious scriptures in the Nyāya System. On the contrary we find such cases as the religious authority seems to delimit the validity of inference. Some inferences are obstructed by an axiom established in the school, whereas others by a ristriction of Brahmanic tradition. In this manner they seemed to protect their whole system from followers of other Schools. By examining this topic I would like to throw a tiny light on the characteristic affinity between philosophy and religion in Indian thought. (shrink)

We examined the effects of unconscious priming on temporal-interval production. In Experiment 1, participants were instructed to keep visual displays on a screen for 2500 ms intervals. Half of the displays were repeated across blocks throughout the entire experiment, and the others were newly generated from trial to trial. The displays consisted of patterns so complex that the participants could not intentionally memorize them. The results showed that significantly more time elapsed for old displays than for new displays before participants (...) indicated that a 2500 ms interval had elapsed. Experiment 2 replicated this effect and excluded an alternative account based on perceived pattern complexity. The effect of repetitive presentation was obtained despite the fact the participants did not recognize the repetition, suggesting that unconscious priming increased temporal production. These results suggest that time perception is affected by an unconscious process. (shrink)

The aim of this paper is to examine the relationship between education and technological rationality from the perspective of the philosophy of education, and to show that while education is deeply related to technique, skills, or technology, it can never be reduced to technical knowledge, and that there are things in education that overflow technical knowledge. I will here ask why there is something in education that overflows technical knowledge — I will define it as knowledge of pathos — and (...) why it is necessary to redefine the meaning of education in terms of knowledge of pathos. In order to address this issue, I will first examine the relationship between technology and transcendence in the world of education in Kei Hachiya’s Education and Transcendence. Second, I will show that recent outstanding theoretical achievements of Japanese philosophers of education — Satoji Yano’s Education from the Perspectives of Gift and Exchange, Yasuo Imai’s Medial Perspective on Education, and Tsunemi Tanaka’s Clinical Theory of Human Becoming — are all located within the problematic area of ‘technology-pathos-education’. Finally, I would like to propose a ‘philosophy of education built on fragile parts’, with a view to redefining education through the knowledge of pathos, paying attention to the experience of pathei mathos and the opportunity of weakness in the philosophy of education. (shrink)

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.

Glivenko-type theorems for substructural logics are comprehensively studied in the paper [N. Galatos, H. Ono, Glivenko theorems for substructural logics over FL, Journal of Symbolic Logic 71 1353–1384]. Arguments used there are fully algebraic, and based on the fact that all substructural logics are algebraizable 279–308] and also [N. Galatos, P. Jipsen, T. Kowalski, H. Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics, in: Studies in Logic and the Foundations of Mathematics, vol. 151, Elsevier, 2007] for the details). As (...) a complementary work to the algebraic approach developed in [N. Galatos, H. Ono, Glivenko theorems for substructural logics over FL, Journal of Symbolic Logic 71 1353–1384], we present here a concise, proof-theoretic approach to Glivenko theorems for substructural logics. This will show different features of these two approaches. (shrink)

This contributed volume includes both theoretical research on philosophical logic and its applications in artificial intelligence, mostly employing the concepts and techniques of modal logic. It collects selected papers presented at the Second Asia Workshop on Philosophical Logic, held in Guangzhou, China in 2014, as well as a number of invited papers by specialists in related fields. The contributions represent pioneering philosophical logic research in Asia.

Both Ambrose St. John (1815–1875) and John Henry Newman (1801–1890), who were received into the Roman Catholic Church in 1845, became members of the Birmingham Oratory. Newman’s closest companion for over three decades, St. John’s death was extremely painful for Newman, not only because it was unexpected, but because of his devotion to Newman as well as his dedication to his spiritual duties. Along with presenting Newman’s narrative of the last few weeks of St. John’s life, this essay raises the (...) question: why did Newman write this “account.”. (shrink)

Prediction is essential for the efficiency of many cognitive processes; however, this process is not always perfect. Predictive coding theory suggests that the brain generates and updates a prediction to respond to an upcoming event. Although an electrophysiological index of prediction, the stimulus preceding negativity, has been reported, it remains unknown whether the SPN reflects the prediction accuracy, or whether it is associated with the prediction error, which corresponds to a mismatch between a prediction and an actual input. Thus, the (...) present study aimed to investigate this question using electroencephalography. Participants were asked to predict the original pictures from pictures that had undergone different levels of pixelation. The SPN amplitude was affected by the level of pixelation and correlated with the subjective evaluation of the prediction accuracy. Furthermore, late positive components were negatively correlated with SPN. These results suggest that the amplitude of SPN reflects the prediction accuracy; more accurate prediction increases the SPN and reduces the prediction error, resulting in reduced LPC amplitudes. (shrink)

We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...) with and is algebraizable, with the variety of residuated lattice-ordered groupoids with unit serving as its equivalent algebraic semantics. Overcoming technical complications arising from the lack of associativity, we introduce a generalized version of a logical matrix and apply the method of quasicompletions to obtain an algebra and a quasiembedding from the matrix to the algebra. By applying the general result to specific cases, we obtain important logical and algebraic properties, including the cut elimination of and various extensions, the strong separation of , and the finite generation of the variety of residuated lattice-ordered groupoids with unit. (shrink)

In this paper, we will develop an algebraic study of substructural propositional logics over FLew, i.e. the logic which is obtained from intuitionistic logics by eliminating the contraction rule. Our main technical tool is to use residuated lattices as the algebraic semantics for them. This enables us to study different kinds of nonclassical logics, including intermediate logics, BCK-logics, Lukasiewicz’s many-valued logics and fuzzy logics, within a uniform framework.

The present paper deals with the predicate version MTL of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono''s Kripke semantics for the predicate version of FLew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL and classical predicate logic is undecidable. Finally, we prove that MTL is complete with respect to the standard semantics, i.e., with respect to Kripke frames on the (...) real interval [0,1], or equivalently, with respect to MTL-algebras whose lattice reduct is [0,1] with the usual order. (shrink)

An emerging concept is that quiescent mature skeletal cells provide an important cellular source for bone regeneration. It has long been considered that a small number of resident skeletal stem cells are solely responsible for the remarkable regenerative capacity of adult bones. However, recent in vivo lineage‐tracing studies suggest that all stages of skeletal lineage cells, including dormant pre‐adipocyte‐like stromal cells in the marrow, osteoblast precursor cells on the bone surface and other stem and progenitor cells, are concomitantly recruited to (...) the injury site and collectively participate in regeneration of the damaged skeletal structure. Lineage plasticity appears to play an important role in this process, by which mature skeletal cells can transform their identities into skeletal stem cell‐like cells in response to injury. These highly malleable, long‐living mature skeletal cells, readily available throughout postnatal life, might represent an ideal cellular resource that can be exploited for regenerative medicine. (shrink)

Along the same line as that in Ono (Ann Pure Appl Logic 161:246–250, 2009), a proof-theoretic approach to Glivenko theorems is developed here for substructural predicate logics relative not only to classical predicate logic but also to arbitrary involutive substructural predicate logics over intuitionistic linear predicate logic without exponentials QFLe. It is shown that there exists the weakest logic over QFLe among substructural predicate logics for which the Glivenko theorem holds. Negative translations of substructural predicate logics are studied by using (...) the same approach. First, a negative translation, called extended Kuroda translation is introduced. Then a translation result of an arbitrary involutive substructural predicate logics over QFLe is shown, and the existence of the weakest logic is proved among such logics for which the extended Kuroda translation works. They are obtained by a slight modification of the proof of the Glivenko theorem. Relations of our extended Kuroda translation with other standard negative translations will be discussed. Lastly, algebraic aspects of these results will be mentioned briefly. In this way, a clear and comprehensive understanding of Glivenko theorems and negative translations will be obtained from a substructural viewpoint. (shrink)

An intermediate predicate logicS + n (n>0) is introduced and investigated. First, a sequent calculusGS n is introduced, which is shown to be equivalent toS + n and for which the cut elimination theorem holds. In § 2, it will be shown thatS + n is characterized by the class of all linear Kripke frames of the heightn.

In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics.