We claim that Proof Systems for natural many-valued logics, whether nite-valued or innnite-valued should be similar in their structure to proof systems of any other natural logic: one should not be able to tell from the structures which are used in a proof system the intended semantics. It is also preferable that standard connectives will be used, with corresponding standard rules. We demonstra...

Three different styles of foundations of mathematics are now commonplace: set theory, type theory, and category theory. How do they relate, and how do they differ? What advantages and disadvantages does each one have over the others? We pursue these questions by considering interpretations of each system into the others and examining the preservation and loss of mathematical content thereby. In...

This paper investigates the connection between temporal logic and the semantics of some temporal expressions in English. Specii-cally, we show how the meanings of English temporal preposition-phrases can be expressed as modal operators in an interval-based temporal logic which we call ETL0. We show how cascaded temporal preposition phrases and temporal preposition phrases with complex complemen...

This paper uses a partially ordered set of syntactic categories to accommodate optionality and licensing in natural language syntax. A complex but well-studied data set pertaining to the syntax of quantifier scope and negative polarity licensing in Hungarian is used to illustrate the proposal. The presentation is geared towards both linguists and logicians. The main ideas can be implemented in ...

The most remarkable feature of Indian formal logic (as it was reflected by the most advanced system of Indian logic, by Navya–Nyaya) is clearly a close connection of a logical formalism to a linguistic material . . . A common characteristic of Indian knowledge on all stages of its existence was a consistent intentionalism, whereas European logic was still a predominantly extentional one. Import...