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In this thesis we present several results about Second-Order Unification. It is well known that the Second-Order Unification Problem is in general undecidable; the frontier between its decidable and undecidable subclasses is thin and it still has not been completely defined. Our purpose is to shed some light on the Second-Order Unification problem and study some of its variants. We have mainly ...

Theoretical Unification in Justice and Beyond The goal of scientific work is to understand more and more by less and less. In this effort, theoretical unification plays a large part. There are two main types of theoretical unification – unification of different theories of the same field of phenomena and unification of theories of different fields of phenomena. Both types are usually a surprise...

By replacing syntactical unification with rigid E-unification, equality handling can be added to rigid variable calculi for first-order logic, including free variable tableau (Fitting, 1996), the mating method (Andrews, 1981), the connection method (Bibel, 1982), and model elimination (Loveland, 1969); for an overview of these calculi, see Chapters I.1.1 and I.1.2. Rigid E-unification and its s...

By replacing syntactical unification with rigid E-unification, equality handling can be added to rigid variable calculi for first-order logic, including free variable tableau (Fitting, 1996), the mating method (Andrews, 1981), the connection method (Bibel, 1982), and model elimination (Loveland, 1969); for an overview of these calculi, see Chapters I.1.1 and I.1.2. Rigid E-unification and its s...

Graph unification is the most expensive part of unification-based grammar parsing. It often takes over 90% of the total parsing time of a sentence. We focus on two speed-up elements in the design of unification algorithms: 1) elimination of excessive copying by only copying successful unifications, 2) Finding unification failures as soon as possible. We have developed a scheme to attain these t...

Nominal unification is an extension of first-order unification that takes into account the α-equivalence relation generated by binding operators, following the nominal approach. We propose a sound and complete procedure for nominal unification with commutative operators, or nominal C-unification for short, which has been formalised in Coq. The procedure transforms nominal C-unification problems...