Subject: SUO: Multimodal reasoning From: "John F. Sowa" Date: Fri, 18 Jul 2003 18:27:50 -0400 To: Chris Menzel CC: IEEE Standard Upper Ontology List Chris, Yes, we are all getting multiple copies (at least 4) of each message to SUO. > Don't worry, John S, I'm not forgetting about you and your modal mayhem! I really hope to commit major mayhem on the reductio ad absurdum that Kripke et al. perpetrated on Leibniz's metaphor of possible worlds. At least Kripke had the decency to admit that he was only using the term as a metaphor, but David L. was one of the worst offenders by taking him literally. However, I am leaving tomorrow to spend a week in Dresden. So I won't be able to respond until I get back next weekend. While I'm gone, I wish you would meditate on the quotations by Dana Scott and John McCarthy about multimodal reasoning. Then look at Cohen & Levesque's song and dance to support three modal operators (at the end of Section 7 in my paper) and tell me how you would represent the semantics of the thousands of verbs for all the speech acts and intentionalities in English. Following are the passages that quote Scott & McCarthy. How would you reply to them? John ________________________________________________________________ That approach cannot represent, much less reason about a sentence that mixes all three modalities, such as _You are never obligated to do anything impossible_. The limitation to just one modality is what Scott (1970) considered "one of the biggest mistakes of all in modal logic": The only way to have any philosophically significant results in deontic or epistemic logic is to combine these operators with: Tense operators (otherwise how can you formulate principles of change?); the logical operators (otherwise how can you compare the relative with the absolute?); the operators like historical or physical necessity (otherwise how can you relate the agent to his environment?); and so on and so on. (p. 143) These philosophical considerations are even more pressing for linguistics, which must relate different modalities in the same sentence. Dunn's semantics facilitates multimodal interactions by allowing each modal operator or each verb that implies a modal operator to have its own associated laws. At the metalevel, laws can be distinguished from facts and from the laws associated with different verbs or operators. At the object level, however, the reasoning process can use first-order logic without distinguishing laws from facts or the laws of one modality from the laws of another. . . . . In his "Notes on Formalizing Context," McCarthy (1993) introduced the predicate ist(C,p), which may be read "the proposition p is true in context C." For clarity, it will be spelled out in the form isTrueIn(C, p). As illustrations, McCarthy gave the following examples: * isTrueIn(contextOf("Sherlock Holmes stories"), "Holmes is a detective"). * isTrueIn(contextOf("U.S. legal history"), "Holmes is a Supreme Court Justice"). In these examples, the context disambiguates the referent of the name Holmes either to the fictional character Sherlock Holmes or to Oliver Wendell Holmes, Jr., the first appointee to the Supreme Court by President Theodore Roosevelt. In effect, names behave like indexicals whose referents are determined by the context. One of McCarthy's reasons for developing a theory of context was his uneasiness with the proliferation of new logics for every kind of modal, temporal, epistemic, and nonmonotonic reasoning. The ever-growing number of modes presented in AI journals and conferences is a throwback to the scholastic logicians who went beyond Aristotle's two modes necessary and possible to permissible, obligatory, doubtful, clear, generally known, heretical, said by the ancients, or written in Holy Scriptures. The medieval logicians spent so much time talking about modes that they were nicknamed the modistae. The modern logicians have axiomatized their modes and developed semantic models to support them, but each theory includes only one or two of the many modes. McCarthy (1977) observed, For AI purposes, we would need all the above modal operators in the same system. This would make the semantic discussion of the resulting modal logic extremely complex. Instead of an open-ended number of modes, McCarthy hoped to develop a simple, but universal mechanism that would replace modal logic with first-order logic supplemented with metalanguage about contexts. That approach can be adapted to Dunn's semantics by adding another predicate isLawOf(C,p), which states that proposition p is a law of context C.