The logic CD is an intermediate logic which exactly corresponds to the Kripke models with constant domains. It is known that the logic CD has a Gentzen-type formulation called LD and rules are replaced by the corresponding intuitionistic rules) and that the cut-elimination theorem does not hold for LD. In this paper we present a modification of LD and prove the cut-elimination theorem for it. Moreover we prove a “weak” version of cut-elimination theorem for LD, saying that all “cuts” except (...) some special forms can be eliminated from a proof in LD. From these cut-elimination theorems we obtain some corollaries on syntactical properties of CD: fragments collapsing into intuitionistic logic. Harrop disjunction and existence properties, and a fact on the number of logical symbols in the axiom of CD. (shrink)

We introduce several restricted versions of the structural rules in the implicational fragment of Gentzen's sequent calculus LJ. For example, we permit the applications of a structural rule only if its principal formula is an implication. We investigate cut-eliminability and theorem-equivalence among various combinations of them. The results include new cut-elimination theorems for the implicational fragments of the following logics: relevant logic E, strict implication S4, and their neighbors (e.g., E-W and S4-W); BCI-logic, BCK-logic, relevant logic R, and the intuitionistic (...) logic. (shrink)

The third author gave a natural deduction style proof system called the \-calculus for implicational fragment of classical logic in. In -calculus, 2015, Post-proceedings of the RIMS Workshop “Proof Theory, Computability Theory and Related Issues”, to appear), the fourth author gave a natural subsystem “intuitionistic \-calculus” of the \-calculus, and showed the system corresponds to intuitionistic logic. The proof is given with tree sequent calculus, but is complicated. In this paper, we introduce some reduction rules for the \-calculus, and give (...) a simple and purely syntactical proof to the theorem by use of the reduction. In addition, we show that we can give a computation model with rich expressive power with our system. (shrink)

The semilattice relevant logics ∪R, ∪T, ∪RW, and ∪TW are defined by semilattice models in which conjunction and disjunction are interpreted in a natural way. For each of them, there is a cut-free labelled sequent calculus with plural succedents . We prove that these systems are equivalent, with respect to provable formulas, to the restricted systems with single succedents . Moreover, using this equivalence, we give a new Hilbert-style axiomatizations for ∪R and ∪T and prove equivalence between two semantics for (...) the contractionless logics ∪RW and ∪TW. (shrink)

We establish the “contraction-elimination theorem” which means that if a sequent Γ A is provable in the implicational fragment of the Gentzen's sequent calculus LK and if it satisfies a certain condition on the number of the occurrences of propositional variables, then it is provable without the right contraction rule. By this theorem, we get the following.1. If an implicational formula A is a theorem of classical logic and is not a theorem of intuitionistic logic, then there is a propositional (...) variable which occurs at least once positively and at least twice negatively in A → a) → a).2. If an implicational formula A is a theorem of intuitionistic logic and is not a theorem of BCK-logic, then there is a propositional variable which occurs at least twice positively and at least once negatively in A → a → b).We prove the contraction-elimination theorem by a fully syntactical method, which has some analogy with Gentzen's cut-elimination. (shrink)

Let ℸ be the set of Gödel numbers Gn of function symbols f such that PRA ⊢ and let γ be the function such that equation imageWe prove: The r. e. set ℸ is m-complete; the function γ is not primitive recursive in any class of functions {f1, f2, ⃛} so long as each fi has a recursive upper bound. This implies that γ is not primitive recursive in ℸ although it is recursive in ℸ.

Barendregt gave a sound semantics of the simple type assignment system λ → by generalizing Tait’s proof of the strong normalization theorem. In this paper, we aim to extend the semantics so that the completeness theorem holds.

Regarding strictly monadic second‐order logic (SMSOL), which is the fragment of monadic second‐order logic in which all predicate constants are unary and there are no function symbols, we show that a standard deductive system with full comprehension is sound and complete with respect to standard semantics. This result is achieved by showing that in the case of SMSOL, the truth value of any formula in a faithful identity‐standard Henkin structure is preserved when the structure is “standardized”; that is, the predicate (...) domain is expanded into the set of all unary relations. In addition, we obtain a simpler proof of the decidability of SMSOL. (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.

Abstract“The wrongness of Albert's action causally explains why Jane judged that his action was wrong”. This type of causal moral explanation has been extensively discussed in the recent metaethical literature. This paper motivates the following claims about this type of moral explanation. First, a typical defence of this type of moral explanation suggested in the literature does not work because it predicts inaccurate modal information. Second, focusing on different aspects of the ways moral judgements are generated provides better chances for (...) the defender of this type of moral explanation. Third, the strategy mentioned in the previous point leads us to the following alternative evaluative explanation: The property of being a harmful action explains a recognisable pattern of moral judgements observed in the relevant empirical studies. One crucial implication the paper alludes to is a localist approach to the debates concerning moral realism: We should consider each moral property's ontological genuineness separately, referring to specific empirical findings that are particularly relevant to the target moral property in question. Such a localist approach can provide solid resources for realists to respond to various anti‐realist challenges, such as an influential evolutionary debunking argument. (shrink)

One influential positive argument for moral realism is the Explanatory Indispensability Argument. A crucial premise of this argument is the explanatory relevance of moral properties. On this premise, moral properties, such as wrongness, rightness, courage, and cowardice, are explanatorily indispensable to some empirical phenomena. Although there has been a lively debate on this premise, one crucial challenge to this thesis, what I call the Scientific Standard Challenge, has not been properly discussed. After explaining this challenge and a related concern, I (...) argue that in response to this central challenge, the proponents of the argument should take what I call the localist turn to defend the explanatory indispensability of moral properties. The localist turn encourages the defenders of moral explanations to be more sensitive to the nature of each moral explanation. For instance, some moral explanations are explanations of social matters, so the standards they need to meet are provided by relevant branches of the social sciences. On the other hand, some other moral explanations are about our psychology, so the theoretical standards those explanations need to meet should come from psychology. I illustrate how this localist project can be conducted in the case of the moral explanation that appeals to injustice. I argue that the field of comparative politics provides the theoretical standards moral explanations of institutional change need to meet. I shall then illustrate how a sophisticated moral explanation can meet those theoretical standards and how this moral explanation can be strong evidence of injustice’s explanatory indispensability. (shrink)

The concept of culture is an integral part of contemporary psychology. However, a mindless use of the concepts and practices traditionally prevalent in academic psychology may lead us into theoretical quandaries borne out of the age old controversy about the nature of psychology as a natural or cultural science. This paper attempts to resolve the quandaries by clarifying a conceptual distinction and relation between interpretive and explanatory psychological theories under a neo-diffusionist metatheory of culture, the view of culture as interpersonally (...) and intrapersonally distributed non-genetically transmitted information. We then outline and advocate both interpretive and explanatory research programs in psychological studies of culture, arguing for 'experimental semiotics' as an interpretive research program in the methodological tradition of experimentation. 2012 APA, all rights reserved). (shrink)

朱子学は現代に生きる私たちにとって価値なきものなのだろうか? 儒教思想と近代的権利概念の親和性に着目、再検証を試みる。.

The most famous chapter of Montesquieu’s _ The Spirit of the Laws _ (1748), Book XI, Chapter 6, 'On the constitution of England,' was an important i nspiration to the creators of modern constitutions, to which they often referred. However, as a result of scholarly focus on the political institutions discussed in this book, Montesquieu’s economic analysis has been woefully neglected. In order to correct this scholarly imbalance, this paper will elucidate the essential significance of Montesquieu’s comparison between the constitution (...) of modern England and that of ancient Rome in Book XI of _ The Spirit of the Laws _ ; inextricable relationship between military and political institutions on the one hand, and the transfer and distribution of wealth on the other. To argue this point, this paper will focus on Montesquieu’s other writings in the same year and shortly after the publication of _ The Spirit of the Laws _ : the revised edition in 1748 of _ The Considerations on the Causes of the Greatness of t... _. (shrink)

We develop intuitionistic public announcement logic over intuitionistic \({\textbf{K}}\), \({{\textbf{K}}}{{\textbf{T}}}\), \({{\textbf{K}}}{{\textbf{4}}}\), and \({{\textbf{S}}}{{\textbf{4}}}\) with distributed knowledge. We reveal that a recursion axiom for the distributed knowledge is _not_ valid for a frame class discussed in [ 12 ] but valid for the restricted frame class introduced in [ 20, 26 ]. The semantic completeness of the static logics for this restricted frame class is established via the concept of pseudo-model.

The present contribution shows that a Hilbert-style axiomatization for dynamic logic of relation changers is complete for the standard Kripke semantics not by a well-known rewriting technique but by the idea of an auxiliary semantics studied by van Benthem and Wang et al. A key insight of our auxiliary semantics for dynamic logic of relation changers can be described as: “relation changers are bounded morphisms.” Moreover, we demonstrate that this semantic insight can be used to provide a modular cut-free labelled (...) sequent calculus for the logic in the sense that our calculus can be regarded as a natural expansion of a labelled sequent calculus of iteration-free propositional dynamic logic. (shrink)

Parochial altruism is manifested in the most violent of conflicts. Although it makes evolutionary sense for kin, many non-kin groups also behave parochially altruistically in response to threat from out-groups. It is possible that such non-kin groups share a sense of “fictive” kinship which encourages them to behave parochially altruistically for each other’s benefit. Our findings show that individuals not directly involved in a conflict approved of parochial altruism enacted by an in-group against an out-group more when the out-group posed (...) a threat to the in-group; however, this effect wasgreaterwhen the in-group members expressed fictive kinship by addressing each other using kinship metaphors such as “brothers.” Furthermore, although males approved of parochial altruism more than females, as the male warrior hypothesis would suggest, the effects of threat and kinship metaphor on approval of parochial altruism applied to both genders. These findings were replicated in an honour and non-honour culture. (shrink)