Task 1. Show that the set of valid formulas of predicate logic is undecidable.

A head predicate is categorized into two types; if the predicate forms a base verb phrase (VP) without its child predicates, the predicate falls into Type 1, and if the

Note: For k ≥ 3, a general CNF formula can easily be converted in polynomial time (in the number of literals) into a k -CNF formula with exactly k literals per clause such that

By assuming each predicate index is used for t authentication sessions, the security was measured in term of the cardinality of the attack set, i.e., the size of the reduced

But the main motivation is that the structural proof theory of deep inference systems for classical logic already differs significantly from that of the sequent calculus and thus

Objects are described by terms that are built from variable, constant and function symbols. Properties and relations are described by formulas that are built from

I Predicate logic is more expressive than propositional logic and allows statements over objects and their properties. I Objects are described by terms that are built from

For instance, the termination predicate algorithms for minus , list minus , and half in the last section were built according to Theorem 3 (where for the sake of brevity we

(i) The (∃ ∗ )-class, containing all FO formulae whose quantifier prefix in prenex normal form only contains existential quantifiers.. Note that relations and functions of any arity