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)

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.

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.

It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part (...) of the paper, we also discuss some extended forms of the Kolmogorov translation and we compare it to the Glivenko translation. (shrink)

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.

Kajiyama has argued that the basis for the concept of _jāti_ (false rejoinder) as described in the _Nyāyasūtra_ is the concept _xiang ying_ (相応) as found in the _Fangbian xin lun_ (方便心論). Kajiyama has also shown that the sophistic arguments called _xiang ying_ are very similar to the _prasaṅga_ arguments of Nāgārjuna, the founder of the Madhyamaka school. It thus seems worthwhile to investigate how later Mādhyamika philosophers treated the concept of _jāti_ that originally appeared as the result of the (...) _Nyāyasūtra’s_ criticism of the concept _xiang ying_ and was later accepted by Buddhist logicians such as Dignāga. This paper shows that there were two entirely opposite Mādhyamika positions regarding the concept of _jāti_. In order to demonstrate this difference, this paper examines in detail statements about _jāti_s that appear in various treatises, especially two works by Bhāviveka and three works by Candrakīrti. As the result, it becomes clear that the differences in the two positions correspond essentially to the differences in how Dignāgaʼs logic was evaluated by the so-called Svātantrika and Prāsaṅgika within the Madhyamaka school. (shrink)

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.

In this paper, a semantics for predicate logics without the contraction rule will be investigated and the completeness theorem will be proved. Moreover, it will be found out that our semantics has a close connection with Beth-type semantics.

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)

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)

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)

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.

A semantical proof of Craig's interpolation theorem for the intuitionistic predicate logic and some intermediate prepositional logics will be given. Our proof is an extension of Henkin's method developed in [4]. It will clarify the relation between the interpolation theorem and Robinson's consistency theorem for these logics and will enable us to give a uniform way of proving the interpolation theorem for them.

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)

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.

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)

This study explores the individual-level activities of legislators in parliament, which have been largely ignored in the literature on parliamentary democracies. Individual legislators are extensively involved in parliamentary activities such as drafting private members’ bills and posing questions, even though these activities have only been considered to play marginal roles in parliamentary democracies. Moreover, their engagement varies significantly. By using unique data from Japan, this study demonstrates that the personal attributes of legislators affect their choice of parliamentary activities. Under electoral (...) systems with intra-party competition, legislators use parliamentary activities as an important means to inform their constituents about what they can do for them and how they differ from other legislators. In elections, candidates cultivate personal votes by exploiting the image drawn from their personal attributes and, once elected, they behave in accordance with their attributes in order to maintain their electoral ground. Thus, they devote themselves to different activities in parliament. The data analyzed here support this argument. The results of empirical analyses show that legislators with local-level political experience engage in particularistic pork-barrel activities that will benefit their local interests, while legislators with legal-work experience allocate their time and energy to general policy-making activities that will enhance their public image and visibility as legal experts. (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)