School of Psychology and Clinical Language Sciences
Divide and…conquer? Towards a non-algorithmic approach to syntax Diego Gabriel Krivochen –
[email protected]
Divide and Conquer: What is it, and what do we use it for?
The Context-Free way: Slashing interpretation out of features
In computer science, divide and conquer (D&C) is an algorithm
CP → wh-NP1 (which violins) S/NP1 ; S/NP1 → NP2 (these sonatas) S/NP1NP2;
design paradigm based on multi-branched recursion. A
S/NP1NP2 → (pro) VP/NP1NP2; VP/NP1NP2 → V NP2/NP2 PP/NP1; NP2/NP2 → ε;
D&C algorithm works by recursively and monotonically breaking down a
PP/NP1 → NP1/NP1; NP1/NP1 → ε;
problem into sub-problems of the same (or a related) type, until these become simple enough to be solved directly. The solutions to the sub-
The Context-Sensitive way: reordering traces
problems are then combined to give a solution to the original problem.
The steps to be followed in a standard D&C algorithm are the following: • Divide a problem of arbitrary complexity into multiple, simpler subproblems, which are usually identical (e.g., for a system of n equations, linear algebra produces n x × y matrices). • Conquer each problem (i.e., solve it), either recursively or straightforwardly (depending on its complexity) • Combine the solutions to address the original problem
D&C in Linguistic Theory
Both transformational and non-transformational grammars are based on D&C:
1)
You did see who → Semantic interpretation
2)
X1 – X2 – X3 – X4 → Structural Description
• Syntactic structure is broken down into smaller pieces (constituents, phrases, words…)
3)
X4 – X2 – X1 – X3 → Structural Change
• Constituents are interpreted locally, in relations within bounded domains
4)
Who did you see? → Morphophonological Structure
• Partial interpretations are put together
Problem: How to get (1) from (4)?
•
Temporal relations are established between main and subordinate events
•
Co-indexed referential expressions are identified
•
Filler-gap dependencies are satisfied
•
…and so on
A little bit more complex… 5)
[Which violins]i are [these sonatas]j difficult to play tj on ti?
The Non-Algorithmic way: (Strawberry) Fields (Forever) D&C approaches have -at least- these problems:
Assuming constituents actually move in syntactic structure, we need to link displaced elements to their original position: that is what traces (t) are there for. We must be able to interpret something along the lines of (5’):
5’) There are some specific sonatas, playing which on certain violins is difficult. I would like to identify the violins.
• Computational cost (thus, cognitive cost) → many steps, not all impact on interpretation • Empirical challenges (some strings cannot be broken down / some strings can be broken down in an infinite number of ways!) • How / where are chunks put back together? There’s also the basic assumption that the mind is essentially a Turing-Machine, which is
• For transformational grammars, semantic interpretation is
controversial –to say the least-
basically a sorting problem, in which a pre-transformational
What if…
phrase marker must be reconstructed from a morphophonological
• We are not dealing with a uniform digital linear computational engine…
structure.
• …but with a field, an analogic dynamical nonlinear system? • Putting chunks together = making field perturbations interfere
• For non-transformational grammars, everything must be encoded in the same representation: filler-gap dependencies are lexical specifications
• Cognitive spaces = topological spaces (metric, non metric…) • This requires different tools: differential equations, Quantum Field Theory, topology…but it can be done. Stay tuned!
