Hiro Uchida, RPI Post Doc

 

Hiro Uchida, RPI Post Doc

Sage 4101

February 8, 2012 12:00 PM - 1:30 PM

 

Abstract:

Enabling reasoning as simulations with concrete objects and relations has a merit of grounding reasoning to more basic perceptual mechanisms. In a hybrid artificial intelligence architecture that uses both logical and non-logical computational methods, the use of simulations for enabling logical inferences allows one to alternate between the logical method and a non-logical one that uses, for example, 3D continuous images as its data-structure. In this talk, we first briefly show that reasoning as simulations can naturally handle modal reasoning that is commonly taken to motivate a standard modal logic language with the diamond and box operators. This result is important, since the presence of the modal operators in the reasoning language causes problems in the above mentioned hybrid AI architecture. We then discuss the expressive power of our modal reasoning as simulations. In proof theoretic logic, it is well-known that propositional logic with the diamond and box operators as above can be faithfully embedded into a first-order logic that is equipped with variables that denote possible worlds, which can then be bound by the usual universal and existential quantifiers. Although such first-order correspondence languages for modal propositional logics allow one to express the empirically useful propositions that modal propositional logics cannot represent, using the full expressive power of such a first-order language loses some of the nice formal properties that modal propositional logics have, such as the decidability of the problem of finding an interpretation model that satisfies a given formula/sequent. In this paper, we show that although reasoning as simulation can formally be as expressive as full-first order logic with quantifiers over world-variables, the current formulation of our simulations, which we believe is the most natural one from the cognitive viewpoint, can maintain the decidability property of the propositional modal logic.

Modal reasoning as simulation

Simulation basics

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