DISTANCES BETWEEN FORMAL THEORIES

Additive Distances and Quasi-Distances Between Words

We study additive distances and quasi-distances between words. We show that every additive distance is finite. We then prove that every additive quasi-distance is regularity-preserving, that is, the neighborhood of any radius of a regular language with respect to an additive quasi-distance is regular. Finally, similar results will be proven for context-free, computable and computably enumerable...

Comparing Formal Cognitive Emotion Theories

We discuss an approach for evaluating cognitive emotion theories that explicitly relies on the use of formal logics of agency. This approach offers various benefits, which range from the fact that a formal logical approach is able to provide an explicit account of the inferential machinery used by an agent to elicit emotions to the fact that logical specifications provide a precise model of wha...

Formal Theories for Logspace Counting

We introduce two-sorted theories in the style of Cook and Nguyen for the complexity classes ParityL and DET, whose complete problems include determinants over GF(2) and Z, respectively. The definable functions in these theories are the functions in the corresponding complexity classes; thus each theory formalizes reasoning using concepts from its corresponding complexity class.

Formal Theories in Fuzzy Logic

Formal Theories for Linear Algebra

We introduce two-sorted theories in the style of [CN10] for the complexity classes ⊕L and DET , whose complete problems include determinants over Z2 and Z, respectively. We then describe interpretations of Soltys’ linear algebra theory LAp over arbitrary integral domains, into each of our new theories. The result shows equivalences of standard theorems of linear algebra over Z2 and Z can be pro...