In this paper, we establish the first-order definability of sequents with consistent variable occurrence on bi-approximation semantics by means of the Sahlqvist–van Benthem algorithm. Then together with the canonicity results in Suzuki (2011), this allows us to establish a Sahlqvist theorem for substructural logic. Our result is not limited to substructural logic but is also easily applicable to other lattice-based logics.
In this paper, we extend the canonicity methodology in Ghilardi & Meloni (1997) to arbitrary lattice expansions, and syntactically describe canonical inequalities for lattice expansions consisting of -meet preserving operations, -multiplicative operations, adjoint pairs, and constants. This approach gives us a uniform account of canonicity for substructural and lattice-based logics. Our method not only covers existing results, but also systematically accounts for many canonical inequalities containing nonsmooth additive and multiplicative uniform operations. Furthermore, we compare our technique with the approach in (...) Dunn et al. (2005) and Gehrke et al. (2005). (shrink)
Homology is a fundamental concept in biology. However, the metaphysical status of homology, especially whether a homolog is a part of an individual or a member of a natural kind, is still a matter of intense debate. The proponents of the individuality view of homology criticize the natural kind view of homology by pointing out that homologs are subject to evolutionary transformation, and natural kinds do not change in the evolutionary process. Conversely, some proponents of the natural kind view of (...) homology argue that a homolog can be construed both as a part of an individual and a member of a natural kind. They adopt the Homeostatic Property Cluster theory of natural kinds, and the theory seems to strongly support their construal. Note that this construal implies the acceptance of essentialism. However, looking back on the history of the concept of homology, we should not overlook the fact that the individuality view was proposed to reject the essentialist interpretation of homology. Moreover, the essentialist notions of natural kinds can, in our view, mislead biologists about the phenomena of homology. Consequently, we need a non-essentialist view of homology, which we name the “persistently reproducible module” view. This view highlights both the individual-like and kind-like aspects of homologs while stripping down both essentialist and anti-essentialist interpretations of homology. In this article, we articulate the PRM view of homology and explain why it is recommended over the other two views. (shrink)
When an agent’s motivation is sensitive to how his supervisor thinks about the agent’s competence, the supervisor has to take into account both informational and expressive contents of her message to the agent. This paper shows that the supervisor can credibly express her trust in the agent’s ability only by being un- clear about what to do. Suggesting what to do, i.e., “directives,” could reveal the supervisor’s “distrust” and reduce the agent’s equilibrium effort level even though it provides useful information (...) about the decision environment. There is also an equilibrium in which directives are neutral in expressive content. However, it is shown that neologism proofness favors equilibria in which directives are double- edged swords. (shrink)
This paper is a comparative study of the propositional intuitionistic (non-modal) and classical modal languages interpreted in the standard way on transitive frames. It shows that, when talking about these frames rather than conventional quasi-orders, the intuitionistic language displays some unusual features: its expressive power becomes weaker than that of the modal language, the induced consequence relation does not have a deduction theorem and is not protoalgebraic. Nevertheless, the paper develops a manageable model theory for this consequence and its extensions (...) which also reveals some unexpected phenomena. The balance between the intuitionistic and modal languages is restored by adding to the former one more implication. (shrink)
We discuss relationships among the existence property, the disjunction property, and their weak variants in the setting of intermediate predicate logics. We deal with the weak and sentential existence properties, and the Z-normality, which is a weak variant of the disjunction property. These weak variants were presented in the author’s previous paper . In the present paper, the Kripke sheaf semantics is used.
Modal counterparts of intermediate predicate logics will be studied by means of algebraic devise. Our main tool will be a construction of algebraic semantics for modal logics from algebraic frames for predicate logics. Uncountably many examples of modal counterparts of intermediate predicate logics will be given.
In this paper, we give a possible characterization of the distributivity on bi-approximation semantics. To this end, we introduce new notions of special elements on polarities and show that the distributivity is first-order definable on bi-approximation semantics. In addition, we investigate the dual representation of those structures and compare them with bi-approximation semantics for intuitionistic logic. We also discuss that two different methods to validate the distributivity—by the splitters and by the adjointness—can be explicated with the help of the axiom (...) of choice as well. (shrink)
Some properties of Kripke-sheaf semantics for super-intuitionistic predicate logics are shown. The concept ofp-morphisms between Kripke sheaves is introduced. It is shown that if there exists ap-morphism from a Kripke sheaf 1 into 2 then the logic characterized by 1 is contained in the logic characterized by 2. Examples of Kripke-sheaf complete and finitely axiomatizable super-intuitionistic (and intermediate) predicate logics each of which is Kripke-frame incomplete are given. A correction to the author's previous paper Kripke bundles for intermediate predicate logics (...) and Kripke frames for intuitionistic modal logics (Studia Logica, 49(1990), pp. 289–306 ) is stated. (shrink)
Since the inception of modern approaches to grammar, Japanese ga has been treated as a marker indicating the grammatical relation `subject.' If this is an accurate characterization of ga, then we would expect ga to occur to mark a grammatical category consisting of `A' and `S'. Our examination of the contexts in which ga is actually used in everyday Japanese conversations shows that this expectation is not borne out. Our findings suggest that it is not appropriate to describe ga in (...) terms of a grammatical relation such as `subject', and that ga may be much less a grammatical marker than a discourse-pragmatic one. (shrink)
One criterion of constructive logics is the disjunction, property (DP). The Halldén-completeness is a weak DP, and is related to the relevance principle and variable separation. This concept is well-understood in the case of propositional logics. We extend this notion to predicate logics. Then three counterparts naturally arise. We discuss relationships between these properties and meet-irreducibility in the lattice of logics.
Negative attitudes toward robots are considered as one of the psychological factors preventing humans from interacting with robots in the daily life. To verify their influence on humans‘ behaviors toward robots, we designed and executed experiments where subjects interacted with Robovie, which is being developed as a platform for research on the possibility of communication robots. This paper reports and discusses the results of these experiments on correlation between subjects’ negative attitudes and their behaviors toward robots. Moreover, it discusses influences (...) of gender and experience of real robots on their negative attitudes and behaviors toward robots. (shrink)