Logic and Computation advanced course:
Logics with Counting.


Course material: pratt-hartmann.pdf


This course presents a survey of decidable fragments of first-order logic with counting quantifiers. Such fragments include: (i) the numerical syllogistic, (ii) the 1-variable fragment with counting, (iii) graded modal logic, (iv) the guarded two-variable fragment with counting and (v) the two-variable fragment with counting. Such logics present special difficulties for the student of computational logic, because their complexity-theoretic analysis often requires specialized techniques. This course will give a comprehensive treatment of these techniques, culminating in a proof that the satisfiability and finite satisfiability problems for the two-variable fragment with counting quantifiers are both NEXPTIME-complete.