In this paper, illocutionary acts of commanding will be differentiated from perlocutionary acts that affect preferences of addressees in a new dynamic logic which combines the preference upgrade introduced in DEUL (dynamic epistemic upgrade logic) by van Benthem and Liu with the deontic update introduced in ECL II (eliminative command logic II) by Yamada. The resulting logic will incorporate J. L. Austin’s distinction between illocutionary acts as acts having mere conventional effects and perlocutionary acts as acts having real effects (...) upon attitudes and actions of agents, and help us understand why saying so can make it so in explicit performative utterances. We will also discuss how acts of commanding give rise to so-called “deontic dilemmas” and how we can accommodate most deontic dilemmas without triggering so-called “deontic explosion”. (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)

Crispin Wright in his 1982 paper argues for strict finitism, a constructive standpoint that is more restrictive than intuitionism. In its appendix, he proposes models of strict finitistic arithmetic. They are tree-like structures, formed in his strict finitistic metatheory, of equations between numerals on which concrete arithmetical sentences are evaluated. As a first step towards classical formalisation of strict finitism, we propose their counterparts in the classical metatheory with one additional assumption, and then extract the propositional part of ‘strict finitistic (...) logic’ from it and investigate. We will provide a sound and complete pair of a Kripke-style semantics and a sequent calculus, and compare with other logics. The logic lacks the law of excluded middle and Modus Ponens and is weaker than classical logic, but stronger than any proper intermediate logics in terms of theoremhood. In fact, all the other well-known classical theorems are found to be theorems. Finally, we will make an observation that models of this semantics can be seen as nodes of an intuitionistic model. (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)

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)

This paper introduces sequent systems for Visser's two propositional logics: Basic Propositional Logic (BPL) and Formal Propositional Logic (FPL). It is shown through semantical completeness that the cut rule is admissible in each system. The relationships with Hilbert-style axiomatizations and with other sequent formulations are discussed. The cut-elimination theorems are also demonstrated by syntactical methods.

We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem isproved (...) in a syntactic way by modifying Gentzen's method. Thisdual-context style system exemplifies the effectiveness of dual-contextformulation in formalizing various non-classical logics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.4 (2003) 50-58 [Access article in PDF] Evolution in Qualitative Factors Used to Evaluate Japanese Students [Tables] Introduction Two basic viewpoints are typically taken in the evaluation of achievement in Japanese schools: either the focus is primarily on "field-content-basedevaluation" or on "ability-concept-based evaluation." I have compared the qualitative factors encompassed by these two viewpoints as reflected in the permanent school records of Japanese students. (...) These recordsinclude classes taken, grades earned, and school-related information. Kanten (in Japanese) has become a key word in the evaluation of academic achievement in Japan. It represents the qualitative factors that should be considered when evaluating a student's learning achievements. In this essay, I review how these qualitative factors have evolved, both for general subjects and for fine arts.From the beginning of the educational system (1872) to 1938, the "assessment" [Hyoutei] of a student depended on the comprehensiveness of the student's achievement in each subject. (Overall assessments are now usually made using a three-point scale; 1-3, a five-point scale; 1-5, or an ABC scale.) However, it was not clearly specified how scholastic ability and learning accomplishment should be assessed or which qualitative factors should be considered.Starting in 1941, teachers were required to evaluate, comprehensively assess, and record the student's learning, consideration, dealing, application, skill, appreciation, practice, and learning attitude through his or her daily learning and activity. 1 The factors seem to be basically equivalent to those recently used as "interest/aspiration/attitude," "thinking," "judgment," [End Page 50] and "expressive power." After 1941, the point of view in the area of fine arts gradually changed from focusing on the "field-content-based factor" to the "ability-concept-based factor" in both the educational content and in evaluation.This report focuses on the evolution in the qualitative factors used in evaluations in the postwar era. From 1949 to 1991 "Understanding," "attitude," and "skill" were specified as factors that shouldbe considered when evaluating a student's learning achievements in 1949. For a few years, these factors were considered independently in the non-referenced evaluation of five-point ratings. The two basic viewpoints, "field-content-based factor" and "ability-concept-based factor," coexisted in the course of study in the early 1950s, according to a tentative plan published in 1951. "Attitude" and "habits" carried the same weight as "understanding" and "skill." These factors received minimal attention at the elementary school level. Evaluations thus evolved from simply an overall assessment of the student's achievement in a subject to an assessment of these specific factors. For instance, at the elementary school level, drawing and handicrafts both had factors related to "field content difference" (for example, drawing, color, and pattern) and to "ability concept difference" (for example, attitude and habit). At the junior high level, the factors were represented by a double-layer structure (Table 1). The elements underlined in Table 1 reflect on the "ability concept difference" (for example, expression activities and understanding activities) instead on the "field content difference." Following the revision of the permanent cumulative records in 1955, students were evaluated based only on an overall assessment of their individual [End Page 51] performance in each subject (Japanese language, mathematics, social studies, music, and drawing and handicrafts). There were three main reasons for this change.The effort it takes to evaluate each factor analytically. The difficulty of evaluating "attitude." The demand by schools at the next level for a comprehensive and uniform evaluation for each student for each subject. 3Furthermore, although "interest" was added as one of factors to be considered in the evaluation, it was not to be dealt with analytically in the evaluation of what the student learned. Consequently, evaluations became clearer and more comprehensive, although the weights of the factors, referred to as the "affective domain," took a step backward. In 1961, the factor "interest/attitude toward fine arts" was added. At the same time, "interest" was given more weight. However, the higher weighting of the factor was short-lived because intangible factors such as... (shrink)

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

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)

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)

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)

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 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)

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)

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)

If the notion of speech acts is to be taken seriously, it must be possible to treat speech acts as acts. The development of systems of DEL (dynamic epistemic logic) in the last two decades suggests an interesting possibility. These systems are developed on the basis of static epistemic logics by introducing model updating operations to interpret various kinds of speech acts including public announcements as well as private information transmissions as what update epistemic states of agents involved. The methods (...) used in developing DEL can be used to develop logics that deal with a much wider variety of speech acts. For example, in ECL (Eliminative Command Logic) of Yamada (2007a) and ECL II of Yamada (2007b), similar model updating operations are introduced tointerpret acts of commanding as what update deontic aspects of the situations in which agents are involved. In Yamada (2008a), ECL II is further extended so as to model acts of promising along with acts of commanding. Moreover, in Yamada (2008b), ECL II is combined with a modified version of DEUL (dynamic epistemic upgrade logic) introduced in van Benthem & Liu (2007). In the resulting logic DDPL (dynamic deontic preference logic), illocutionary acts of commanding are differentiated from preference upgrading perlocutionary acts. The development of these logics suggests a recipe for developing logics that deal with various specific speech acts: first, carefully identify the aspects affected by the speech acts you want to study; second, find the modal logic that characterizes the aspects in question; and finally, add dynamic modalities that stand for the types of the speech acts being studied and define model updating operation that interprets these speech acts as what update the very aspects. (shrink)

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)

There are three main points of the paper. 1. There are straightforward ways of manipulating expected gains and losses that result in a divergence between fair betting odds and credence. Such manipulations are familiar from tools of finance. One can easily see that the Sleeping Beauty case is structured in such a way as to result in a divergence between fair betting odds and credence. 2. The inspection of credences and betting odds in certain betting situations shows that the two (...) main extant positions, Elga's and Lewis's, are both mistaken. 3. My proposal may seem to require a revision of probability theory but it does not. The Sleeping Beauty case merely calls attention to a constraint on partitioning of possibility space that is usually satisfied as a matter of course but can in fact be violated. (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.

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.4 (2003) 50-58 [Access article in PDF] Evolution in Qualitative Factors Used to Evaluate Japanese Students [Tables] Introduction Two basic viewpoints are typically taken in the evaluation of achievement in Japanese schools: either the focus is primarily on "field-content-basedevaluation" or on "ability-concept-based evaluation." I have compared the qualitative factors encompassed by these two viewpoints as reflected in the permanent school records of Japanese students. (...) These recordsinclude classes taken, grades earned, and school-related information. Kanten (in Japanese) has become a key word in the evaluation of academic achievement in Japan. It represents the qualitative factors that should be considered when evaluating a student's learning achievements. In this essay, I review how these qualitative factors have evolved, both for general subjects and for fine arts.From the beginning of the educational system (1872) to 1938, the "assessment" [Hyoutei] of a student depended on the comprehensiveness of the student's achievement in each subject. (Overall assessments are now usually made using a three-point scale; 1-3, a five-point scale; 1-5, or an ABC scale.) However, it was not clearly specified how scholastic ability and learning accomplishment should be assessed or which qualitative factors should be considered.Starting in 1941, teachers were required to evaluate, comprehensively assess, and record the student's learning, consideration, dealing, application, skill, appreciation, practice, and learning attitude through his or her daily learning and activity. 1 The factors seem to be basically equivalent to those recently used as "interest/aspiration/attitude," "thinking," "judgment," [End Page 50] and "expressive power." After 1941, the point of view in the area of fine arts gradually changed from focusing on the "field-content-based factor" to the "ability-concept-based factor" in both the educational content and in evaluation.This report focuses on the evolution in the qualitative factors used in evaluations in the postwar era. From 1949 to 1991 "Understanding," "attitude," and "skill" were specified as factors that shouldbe considered when evaluating a student's learning achievements in 1949. For a few years, these factors were considered independently in the non-referenced evaluation of five-point ratings. The two basic viewpoints, "field-content-based factor" and "ability-concept-based factor," coexisted in the course of study in the early 1950s, according to a tentative plan published in 1951. "Attitude" and "habits" carried the same weight as "understanding" and "skill." These factors received minimal attention at the elementary school level. Evaluations thus evolved from simply an overall assessment of the student's achievement in a subject to an assessment of these specific factors. For instance, at the elementary school level, drawing and handicrafts both had factors related to "field content difference" (for example, drawing, color, and pattern) and to "ability concept difference" (for example, attitude and habit). At the junior high level, the factors were represented by a double-layer structure (Table 1). The elements underlined in Table 1 reflect on the "ability concept difference" (for example, expression activities and understanding activities) instead on the "field content difference." Following the revision of the permanent cumulative records in 1955, students were evaluated based only on an overall assessment of their individual [End Page 51] performance in each subject (Japanese language, mathematics, social studies, music, and drawing and handicrafts). There were three main reasons for this change.The effort it takes to evaluate each factor analytically. The difficulty of evaluating "attitude." The demand by schools at the next level for a comprehensive and uniform evaluation for each student for each subject. 3Furthermore, although "interest" was added as one of factors to be considered in the evaluation, it was not to be dealt with analytically in the evaluation of what the student learned. Consequently, evaluations became clearer and more comprehensive, although the weights of the factors, referred to as the "affective domain," took a step backward. In 1961, the factor "interest/attitude toward fine arts" was added. At the same time, "interest" was given more weight. However, the higher weighting of the factor was short-lived because intangible factors such as... (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].

We consider iterations of general elementary embeddings and, using this notion, point out helices of consistency-wise implications between large large cardinals.Up to now, large cardinal properties have been considered as properties which cannot be accessed by any weaker properties and it has been known that, with respect to this relation, they form a proper hierarchy. The helices we point out significantly change this situation: the same sequence of large cardinal properties occurs repeatedly, changing only the parameters.As results of our investigation (...) of this helical structure, we have new characterizations of extendible cardinals and of Vopěnkan cardinals in terms of elementary embeddings from the universe V, a new large large cardinal property which looks like Shelahness properly between Vopěnkaness and almost hugeness, and a more direct relation between Vopěnkaness and Woodinness than already known.We also consider limits of the helices and relations with the axioms I1–I3. (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)

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 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)