Section: Scientific Foundations
From programming languages to linguistic grammars
Participants : Pierre Boullier, Éric Villemonte de La Clergerie, Benoît Sagot.
- MCS formalisms
Mildly Context-Sensitive formalisms are a class of formalisms that is stricly more powerful than CFGs, but stricly less powerful than formalisms that cover the class of all languages recognizable in polynomial time
Historically, several members of Alpage were originally specialists in the domain of modeling and parsing for programming languages, and are working for more than 10 years on the generalization and extension of the techniques involved to the domain of natural language. The shift from programming language grammars to NLP grammars seriously increases complexity and requires ways to handle the ambiguities inherent in every human language. It is well known that these ambiguities are the sources of many badly handled combinatorial explosions.
Furthermore, while most programming languages are expressed by (subclasses) of well-understood context-free grammars (CFGs), no consensual grammatical formalism has yet been accepted by the whole linguistic community for the description of human languages. On the contrary, new formalisms (or variants of older ones) appear constantly. Many of them may be classified into the three following large families:
- Mildly Context-Sensitive (MCS) formalisms
They manipulate possibly complex elementary structures with enough restrictions to ensure the possibility of parsing with polynomial time complexities. They include, for instance, Tree Adjoining Grammars (TAGs) and Multi-component TAGs with trees as elementary structures, Linear Indexed Grammars (LIGs). Although they are strictly more powerful than MCS formalisms, Range Concatenation Grammars (RCGs, introduced and used by Alpage members, such as Pierre Boullier and Benoît Sagot  ,  ,  ) are also parsable in polynomial time.
- Unification-based formalisms
They combine a context-free backbone with logic arguments as decoration on non-terminals. Most famous representatives are Definite Clause Grammars (DCGs) where PROLOG powerful unification is used to compute and propagate these logic arguments. More recent formalisms, like Lexical Functional Grammars (LFGs) and Head-Driven Phrasal Structure Grammars (HPSGs) rely on more expressive Typed Feature Structures (TFS) or constraints.
- Unification-based formalisms with an MCS backbone
The two above-mentioned characteristics may be combined, for instance by adding logic arguments or constraints to non-terminals in TAGs.
However, despite this diversity, convergences may be found between these formalisms and most of them take place in a so-called Horn continuum, i.e. a set of formalisms with increasing complexities, ranging from Propositional Horn Clauses to first-order Horn Clauses (roughly speaking equivalent to PROLOG), and even beyond.