Varieties of Monadic Heyting Algebras. Part I

This paper deals with the varieties of monadic Heyting algebras, algebraic models of intuitionistic modal logic MIPC. We investigate semisimple, locally finite, finitely approximated and splitting varieties of monadic Heyting algebras as well as varieties with the disjunction and the existence properties. The investigation of monadic Heyting algebras clarifies the correspondence between intuitionistic modal logics over MIPC and superintuitionistic predicate logics and provides us with the solutions of several problems raised by Ono [35].     

Influence of vowel context on the audio‐visual speech perception of voiced stop consonants

The work reported here investigated whether the extent of McGurk effect differs according to the vowel context, and differs when cross‐modal vowels are matched or mismatched in Japanese. Two audio‐visual experiments were conducted to examine the process of audio‐visual phonetic‐feature extraction and integration. The first experiment was designed to compare the extent of the McGurk effect in Japanese in three different vowel contexts. The results indicated that the effect was largest in the /i/ context, moderate in the /a/ context, and almost nonexistent in the /u/ context. This suggests that the occurrence of McGurk effect depends on the characteristics of vowels and the visual cues from their articulation. The second experiment measured the McGurk effect in Japanese with cross‐modal matched and mismatched vowels, and showed that, except with the /u/ sound, the effect was larger when the vowels were matched than when they were mismatched. These results showed, again, that the extent of McGurk effect depends on vowel context and that auditory information processing before phonetic judgment plays an important role in cross‐modal feature integration.     

PHONOLOGY IN THE LEXICAL PROCESSING OF CHINESE: PRIMING TONE NEIGHBOURS

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A Note on Graded Modal Logic

We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results.     

Skepticism and Epistemic Logic

This essay attempts to implement epistemic logic through a non-classical inference relation. Given that relation, an account of '(the individual) a knows that A' is constructed as an unfamiliar non-normal modal logic. One advantage to this approach is a new analysis of the skeptical argument.     

On Fork Arrow Logic and its Expressive Power

We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order correspondence language, so both can express the same input–output behavior of processes.     

De Re Language,De Re Eliminability,and the Essential Limits of Both

De re modality is eliminable if there is an effective translation of all wffs into non-de re equivalents. We cannot have logical equivalence unless logic has odd theses, but we can have material equivalence by banning all essences, something the non-de re facts let us do, or by giving everything such humdrum essences as self-identity and banning the more interesting ones. Eliminability cannot be got from weaker assumptions, nor independent ones of even modest generality. The net philosophical import is that, quite apart from the merits of essentialism, de re language has scant utility.     

Propositions, Sets, and Worlds

If we agree with Michael Jubien that propositions do not exist, while accepting the existence of abstract sets in a realist mathematical ontology, then the combined effect of these ontological commitments has surprising implications for the metaphysics of modal logic, the ontology of logically possible worlds, and the controversy over modal realism versus actualism. Logically possible worlds as maximally consistent proposition sets exist if sets generally exist, but are equivalently expressed as maximally consistent conjunctions of the same propositions in corresponding sets. A conjunction of propositions, even if infinite in extent, is nevertheless itself a proposition. If sets and hence proposition sets exist but propositions do not exist, then whether or not modal realism is true depends on which of two apparently equivalent methods of identifying, representing, or characterizing logically possible worlds we choose to adopt. I consider a number of reactions to the problem, concluding that the best solution may be to reject the conventional model set theoretical concept of logically possible worlds as maximally consistent proposition sets, and distinguishing between the actual world alone as maximally consistent and interpreting all nonactual merely logically possible worlds as submaximal. I am grateful to the Netherlands Institute for Advanced Study in the Humanities and Social Sciences (NIAS), Royal Netherlands Academy of Arts and Sciences (KNAW), for supporting this among related research projects in philosophical logic and philosophy of mathematics during my Resident Research Fellowship in 2005-2006.