In this work, we wish to determine the complexity of deciding whether a given multiset of symbols, chosen from some finite set of symbols, can be derived according to the rules of a given context-free grammar. Providing an upper bound for this problem is of interest to computational linguistics, one goal of which is to classify the complexity of parsing and understanding natural language. We co...

This thesis focuses on automatic theorem proving. In this area there is usually a tradeoff between the "generality" of a prover and the amount of user-guidance it requires to find a proof. This thesis demonstrates that the amount of guidance needed can be reduced by employing reasoning procedures for specialized theories. It presents an enhancement to the Larch Prover (LP) with specialized theo...

Ordered semantic hyper-linking (OSHL) is a theorem prover for first-order logic that generates models and uses them to instantiate first-order clauses to ground clauses, and applies a propositional prover to these ground clauses. OSHL-U extends OSHL with rules for unit clauses and with heuristics. The unit rules in OHSL-U are designed to minimize the use of blind instantiation to generate groun...

We consider proof systems for effectively propositional logic. First, we show that propositional resolution for effectively propositional logic may have exponentially longer refutations than resolution for this logic. This shows that methods based on ground instantiation may be weaker than non-ground methods. Second, we introduce a generalisation rule for effectively propositional logic and sho...

We rst embed Pearce s equilibrium logic and Ferraris s propositional general logic programs in Lin and Shoham s logic of GK a nonmonotonic modal logic that has been shown to include as special cases both Reiter s default logic in the propositional case and Moore s autoepistemic logic From this embedding we obtain a mapping from Ferraris s propositional general logic programs to circumscription ...

A framework is developed that extends Hilbert-style proof systems for propositional and modal logics to comprehend their team-based counterparts. The method is applied to classical propositional logic and the modal logic K. Complete axiomatizations for their team-based extensions, propositional team logic PTL and modal team logic MTL, are presented. 1998 ACM Subject Classification F.4.1 Mathema...

The purpose of this note is to suggest an alternative explanation of the relationship between predicate logics with equality and linear logic. The explanation given by Girard resorts to so called exponentials, which are believed to extract from a linear formula A its classical content !A and ?A. Thus, Girard gives a top-down explanation of the relationship between linear and classical logics: t...

A great deal of insight about a logic can be derived from the study of the diiculty of deciding if a given formula is provable in that logic. Most rst order logics are undecidable and are linear time decidable with no quantiiers and no propositional symbols. However , logics diier greatly in the complexity of deciding propositional formulas. For example, rst-order classical logic is undecidable...