One prominent feature of belief is that a belief cannot be formed at will. This paper argues that the best explanation of this fact is that belief formation is a process that takes aim at the truth. Taking aim at the truth is to be understood as causal responsiveness of the processes constituting belief formation to what facilitates achieving true beliefs. The requirement for this responsiveness precludes the possibility of belief formation responding to intentions in a way that would count (...) as forming a belief at will. (shrink)

Roelcke non-precompactness, simplicity, and non-amenability of the automorphism group of the Fraïssé limit of finite Heyting algebras are proved among others.

We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; (...) this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy. (shrink)

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditionalω. Namely, the equivalence between normal transfinite recursion scheme and newdependent transfinite recursionscheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universeVof sets is treated as the given (...) totality. (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)

This paper presents the first dataset for Japanese Legal Judgment Prediction (LJP), the Japanese Tort-case Dataset (JTD), which features two tasks: tort prediction and its rationale extraction. The rationale extraction task identifies the court’s accepting arguments from alleged arguments by plaintiffs and defendants, which is a novel task in the field. JTD is constructed based on annotated 3477 Japanese Civil Code judgments by 41 legal experts, resulting in 7978 instances with 59,697 of their alleged arguments from the involved parties. Our (...) baseline experiments show the feasibility of the proposed two tasks, and our error analysis by legal experts identifies sources of errors and suggests future directions of the LJP research. (shrink)

In his previous work, the author has introduced the axiom schema of inductive dichotomy, a weak variant of the axiom schema of inductive definition, and used this schema for elementary ) positive operators to separate open and clopen determinacies for those games in which two players make choices from infinitely many alternatives in various circumstances. Among the studies on variants of inductive definitions for bounded ) positive operators, the present article investigates inductive dichotomy for these operators, and applies it to (...) constructive investigations of variants of determinacy statements for those games in which the players make choices from only finitely many alternatives. As a result, three formulations of open determinacy, that are all classically equivalent with each other, are equivalent to three different semi-classical principles, namely Markov’s Principle, Lesser Limited Principle of Omniscience and Limited Principle of Omniscience, over a suitable constructive base theory that proves clopen determinacy. Open and clopen determinacies for these games are thus separated. Some basic results on variants of inductive definitions for \ positive operators will also be given. (shrink)

This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some forms of the reflection principle, (...) are also presented. The equivalence results among systems of truth and classes obtained in this article are summarized in Theorem 104 , Theorem 107 and Theorem 108. (shrink)

Truth is often considered to be a logico-linguistic tool for expressing indirect endorsements and infinite conjunctions. In this article, I will point out another logico-linguistic function of truth: to enable and validate what I call a blind argument, namely, an argument that involves indirectly endorsed statements. Admitting this function among the logico-linguistic functions of truth has some interesting consequences. In particular, it yields a new type of so-called conservativeness argument, which poses a new type of threat to deflationism about truth.

We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies have been extensively studied, we point out that well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting α⊢wfwhereα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_\alpha \vdash \mathsf{wf}\, {\rm where}\, _\alpha}$$\end{document} stands for the iteration of Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^0_1}$$\end{document} comprehension along some ordinal α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha}$$\end{document} and wf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{wf}}$$\end{document} stands for the well-foundedness of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha}$$\end{document}. (shrink)

The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA0, those in second order set theory extending NBG are. In this article, we establish the equivalence between Δ01-LFP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^1_0\mbox{\bf-LFP}}$$\end{document} and Δ01-FP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta^1_0\mbox{\bf-FP}}$$\end{document}, which assert the existence of a least and of a fixed point, respectively, for positive elementary operators. Our proof also shows (...) the equivalence between ID1 and ID^1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\widehat{\it ID}_1}$$\end{document}, both of which are defined in the standard way but with the starting theory PA replaced by ZFC. (shrink)

We introduce a new simple way of defining the forcing method that works well in the usual setting under FA, the Foundation Axiom, and moreover works even under Aczel's AFA, the Anti-Foundation Axiom. This new way allows us to have an intuition about what happens in defining the forcing relation. The main tool is H. Friedman's method of defining the extensional membership relation ∈ by means of the intensional membership relation ε .Analogously to the usual forcing and the usual generic (...) extension for FA-models, we can justify the existence of generic filters and can obtain the Forcing Theorem and the Minimal Model Theorem with some modifications. These results are on the line of works to investigate whether model theory for AFA-set theory can be developed in a similar way to that for FA-set theory.Aczel pointed out that the quotient of transition systems by the largest bisimulation and transition relations have the essentially same theory as the set theory with AFA. Therefore, we could hope that, by using our new method, some open problems about transition systems turn out to be consistent or independent. (shrink)

We present a version of Herbelin’s image-calculus in the call-by-name setting to study the precise correspondence between normalization and cut-elimination in classical logic. Our translation of λμ-terms into a set of terms in the calculus does not involve any administrative redexes, in particular η-expansion on μ-abstraction. The isomorphism preserves β,μ-reduction, which is simulated by a local-step cut-elimination procedure in the typed case, where the reduction system strictly follows the “ cut=redex” paradigm. We show that the underlying untyped calculus is confluent (...) and enjoys the PSN property for the isomorphic image of λμ-calculus, which in turn yields a confluent and strongly normalizing local-step cut-elimination procedure for classical logic. (shrink)

We consider two variants of transfinite induction, one with monotonicity assumption on the predicate and one with the induction hypothesis only for cofinally many below. The latter can be seen as a transfinite analogue of the successor induction, while the usual transfinite induction is that of cumulative induction. We calculate the supremum of ordinals along which these schemata for \ formulae are provable in \. It is shown to be larger than the proof-theoretic ordinal \ by power of base 2. (...) We also show a similar result for the structural transfinite induction, defined with fundamental sequences. (shrink)

The conservativeness argument poses a dilemma to deflationism about truth, according to which a deflationist theory of truth must be conservative but no adequate theory of truth is conservative. The debate on the conservativeness argument has so far been framed in a specific formal setting, where theories of truth are formulated over arithmetical base theories. I will argue that the appropriate formal setting for evaluating the conservativeness argument is provided not by theories of truth over arithmetic but by those over (...) subject matters ‘richer’ than arithmetic, such as set theory. The move to this new formal setting provides deflationists with better defence and brings a broader perspective to the debate. (shrink)

Distracted attention is considered responsible for most car accidents, and many functional magnetic resonance imaging researchers have addressed its neural correlates using a car-driving simulator. Previous studies, however, have not directly addressed safe driving performance and did not place pedestrians in the simulator environment. In this fMRI study, we simulated a pedestrian-rich environment to explore the neural correlates of three types of safe driving performance: accurate lane-keeping during driving, the braking response to a preceding car, and the braking response to (...) a crossing pedestrian. Activation of the bilateral frontoparietal control network predicted high driving accuracy. On the other hand, activation of the left posterior and right anterior superior temporal sulci preceding a sudden pedestrian crossing predicted a slow braking response. The results suggest the involvement of different cognitive processes in different components of driving safety: the facilitatory effect of maintained attention on driving accuracy and the distracting effect of social–cognitive processes on the braking response to pedestrians. (shrink)

This paper describes an automatic monitoring system that constantly checks partial update in Web pages and notifies them to a user. While one of the most important advantages of the WWW is update of Web pages, we need to constantly check them out and this task takes much cognitive load. Thus applications to automatically check update of Web pages have been developed, however they can not deal with partial update like update in a particular cell in a table in a (...) Web page. Hence we developed a automatic monitoring system that checks such partial update. A user can give a system regions in which he/she wants to know the update in a Web page as training examples, and it is able to learn rules to identify the partial update by classification learning. By this learning, a user do not need to directly describe the rules. We implemented our system and some executed examples were presented. (shrink)

In this paper, we develop an organization method of page information agents for adaptive interface between a user and a Web search engine. Though a Web search engine indicates a hit list of Web pages to user’s query using a large database, they includes many useless ones. Thus a user has to select useful Web pages from them with page information indicated on the hit list, and actually fetch the Web page for investigating the relevance. Unfortunately, since the page information (...) on a hit list is neither sufficient nor necessary for a user, the adequate information is necessary for valid selection. However which information is adequate depends on a user and a task. Hence we propose adaptive interface AOAI in which different page information agents are organized through man-machine interaction. In AOAI, the page information agents indicating different page information on a hit list like the file-size, network traffic and a page title are prepared at first. A user evaluates them through searching with a search engine, and the agents are organized based on the evaluation. As results, different organizations are achieved depending on a user and a task. Finally we make experiments with subjects and find out AOAI is promising for adaptive interface between a user and a search engine. (shrink)

Developmental research suggests that young children tend to value dominant individuals over subordinates. This research, however, has nearly exclusively been carried out in Western cultures, and cross-cultural research among adults has revealed cultural differences in the valuing of dominance. In particular, it seems that Japanese culture, relative to many Western cultures, values dominance less. We conducted two experiments to test whether this difference would be observed in preschoolers. In Experiment 1, preschoolers in France and in Japan were asked to identify (...) with either a dominant or a subordinate. French preschoolers identified with the dominant, but Japanese preschoolers were at chance. Experiment 2 revealed that Japanese preschoolers were more likely to believe a subordinate than a dominant individual, both compared to chance and compared to previous findings among French preschoolers. The convergent results from both experiments thus reveal an early emerging cross-cultural difference in the valuing of dominance. (shrink)

Although dual-process or divided-mind models of self-control dominate the literature, they suffer from empirical and conceptual challenges. We propose an alternative approach, suggesting that self-control can be characterized by a fragmented part versus integrated whole dynamic. Whereas responses to events derived from fragmented parts of the mind undermine self-control, responses to events derived from integrated wholes enhance self-control. We review empirical evidence from psychology and related disciplines that support this model. We, moreover, discuss the implications of this work for psychology, (...) neuroscience, economics, and philosophy. In particular, we highlight how this model addresses many of the conceptual and empirical short-comings of divided-mind models. We suggest that understanding self-control as the interplay between fragmented parts versus integrated wholes, moreover, provides novel insights and testable new hypotheses. (shrink)

In this article we study the systems KF and VF of truth over set theory as well as related systems and compare them with the corresponding systems over arithmetic.

We study filters in residuated structures that are associated with congruence relations (which we call -filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters. We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of -filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters will turn out to coincide with truth sets under various (...) well known semantics for certain substructural logics. We also investigate which structural rules are needed to interpret each connective in terms of prime -filters in the same way as in Kripke or Routley-Meyer semantics. We may consider that the set of the structural rules that each connective needs in this sense reflects the difficulty of giving the meaning of the connective. A surprising discovery is that connectives , ⅋ of linear logic are linearly ordered in terms of the difficulty in this sense. (shrink)

Classes are the objects of the second sort of second-order set theory. They have sets as their members and behave like sets, but paradoxes tell us that many classes cannot be sets. Then, what are classes? Predicativism about classes suggests that classes are predicates of sets, and this article investigates the question from the predicativist point of view in light of recent developments in the use of classes in set theory. Predicativism has been considered too restrictive and unable to accommodate (...) the use of classes in set theory. This diagnosis, however, is only true of a certain specific type of predicativism. In this article, we propose a new type of predicativism, which we call liberal predicativism, and argue that predicativism is still a highly viable option, and our liberal version provides a sufficiently versatile and workable nominalist concept of classes for set theory. (shrink)

We investigate the role of coalgebraic predicate logic, a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt–Thomason theorem and Fine’s canonicity theorem for classes of monotonic neighborhood frames closed under elementary equivalence in coalgebraic predicate logic. The elementary equivalence here can be relativized to the classes of monotonic, quasi-filter, augmented quasi-filter, filter, or augmented filter neighborhood frames, respectively. The original, Kripke-semantic versions of the theorems follow as a (...) special case concerning the classes of augmented filter neighborhood frames. (shrink)

We measure, in the presence of the axiom of infinity, the proof-theoretic strength of the axioms of set theory which make the theory look really like a “theory of sets”, namely, the axiom of extensionality Ext, separation axioms and the axiom of regularity Reg . We first introduce a weak weak set theory as a base over which to clarify the strength of these axioms. We then prove the following results about proof-theoretic ordinals:1. and ,2. and . We also show (...) that neither Reg nor affects the proof-theoretic strength, i.e., where T is Basic plus any combination of Ext and. (shrink)

By obtaining several new results on Cook-style two-sorted bounded arithmetic, this paper measures the strengths of the axiom of extensionality and of other weak fundamental set-theoretic axioms in the absence of the axiom of infinity, following the author’s previous work [K. Sato, The strength of extensionality I — weak weak set theories with infinity, Annals of Pure and Applied Logic 157 234–268] which measures them in the presence. These investigations provide a uniform framework in which three different kinds of reverse (...) mathematics–Friedman–Simpson’s “orthodox” reverse mathematics, Cook’s bounded reverse mathematics and large cardinal theory–can be reformulated within one language so that we can compare them more directly. (shrink)

Prior's three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic $Q_t $ and give its axiomatization and semantics. We also argue that $Q_t $ provides a smooth solution to the problem of future contingents.

Following the finitist’s rejection of the complete totality of the natural numbers, a finitist language allows only propositional connectives and bounded quantifiers in the formula-construction but not unbounded quantifiers. This is opposed to the currently standard framework, a first-order language. We conduct axiomatic studies on the notion of truth in the framework of finitist arithmetic in which at least smash function $\#$ is available. We propose finitist variants of Tarski ramified truth theories up to rank $\omega $, of Kripke–Feferman truth (...) theory and of Friedman–Sheard truth theory, and show that all of these have the same strength as the finitist arithmetic of one higher level along Grzegorczyk hierarchy. On the other hand, we also show that adding Burgess-style groundedness schema, adjusted to the finitist setting, makes Kripke–Feferman truth theory as strong as primitive recursive arithmetic. Meanwhile, we obtain some basic results on finitist theories of (full and hat) inductive definitions and on the second order axiom of hat inductive definitions for positive operators. (shrink)

We introduce a dual-context style sequent calculus which is complete with respectto Kripke semantics where implication is interpreted as strict implication in the modal logic K. The cut-elimination theorem for this calculus is proved by a variant of Gentzen's method.

This paper studies several systems of the transfinite iteration and autonomous progression of self-applicable truth and determines their proof-theoretic strength.