Abstract
Natural recursion in syntax is recursion by linguistic value, which is not syntactic in nature but semantic. Syntax-specific recursion is not recursion by name as the term is understood in theoretical computer science. Recursion by name is probably not natural because of its infinite typeability. Natural recursion, or recursion by value, is not species-specific. Human recursion is not syntax-specific. The values on which it operates are most likely domain-specific, including those for syntax. Syntax seems to require no more (and no less) than the resource management mechanisms of an embedded push-down automaton (EPDA). We can conceive EPDA as a common automata-theoretic substrate for syntax, collaborative planning, i-intentions, and we-intentions. They manifest the same kind of dependencies. Therefore, syntactic uniqueness arguments for human behavior can be better explained if we conceive automata-constrained recursion as the most unique human capacity for cognitive processes.
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Notes
- 1.
All but one, that is. Everett (2005) argues that recursion is not a fact for all languages. That may be true, but the fact remains that some languages do have it, and all languages are equally likely to be acquirable. See Nevins et al. (2009) and Bozsahin (2012) for some criticism of Everett, and his response to some of the criticisms (Everett 2009). Even when syntactic recursion is not attested, there seems little doubt that semantic recursion, or recursion by value, is common for all humans, e.g. the ability to think where thinker is agent and thinkee is another thought of same type, manifested in English with complement clauses such as I think she thinks you like me. But, it can be expressed nonrecursively as well: I think of the following: she thinks of it; it being that you like me. We shall have a closer look at such syntactic, semantic and anaphoric differences in recursive thoughts.
- 2.
The name is apt because, as lambda-calculus has shown us, reentrant knowledge can be captured without names if we want to, and that the solution comes with a price (more on that later). In current work, the term recursion by name (or label) is taken in its technical sense in computer science. Confusion will arise when we see the same term in linguistics, for example most recently in Chomsky (2013), where use of the same label in a recursive merger refers to the term ‘label’ in a different sense, to occurrence of a value.
- 3.
- 4.
- 5.
I am not suggesting that (12) is the universal schema for all plans. It is meant to show that collaborative plans may be LIG-serializable. LIG-plan space remains to be worked out. For example, base cases of individuated grammars, the \(S_{i}^{{\prime}}[S_{i}]\) rules, doing running—as part of a dance—and Ai would be by definition LIG-serializable too, but in a manner different than what α and β are intended to capture, viz. contextualized knowledge states of the group constituting the we-intention. Ais may be LIG-realized action sequences, making the whole collection a we-plan.
- 6.
We note that the language {ww∣w ∈ { a, b, c}∗} is fundamentally different than double-copy {www∣w ∈ { a, b, c}∗}. The first one allows stack processing. Here is a LIG grammar for it: \(S_{[\ldots ]} \rightarrow x\ S_{[x\ldots ]},S_{[\ldots ]} \rightarrow S_{[\ldots ]}^{{\prime}},S_{[x\ldots ]}^{{\prime}}\rightarrow \ S_{[\ldots ]}^{{\prime}}\ x,S_{[\ ]}^{{\prime}}\rightarrow \epsilon\), for x ∈ { a, b, c}.
- 7.
Continuing in this way of thinking, we could factor recursion and other dependencies in a grammar, and incorporate word order as a lexically specifiable constraint. It might achieve the welcome result of self-constraining recursion and levels of embedding in parsing: see Joshi (2004: 662).
Both LTAG and CCG avoid recursion by name, LTAG by employing adjunction in addition to substitution, and CCG by avoiding any use of paradoxical combinators such as Y, or generalized composition. That is how they stay well below Turing equivalence that might otherwise have been achieved because of recursion by name; see also Joshi (1990), Vijay-Shanker and Weir (1993), and Bozsahin (2012) for discussion of these aspects. Their restrictiveness (to LIG) becomes their explanatory force.
- 8.
The Swiss German facts are more direct because the language has overt case marking and more strict word order; see Bozsahin (2012) for a CCG grammar of some Swiss German examples.
- 9.
Notice that \(\{a^{n}b^{n}c^{n}d^{n}e^{n}\mid n \geq 0\}\) is not a linear-indexed language, hence such grammars make no use of a linear distance metric, or simple induction from patterns; see Joshi (1983).
- 10.
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Acknowledgements
Thanks to PT-AI reviewers and the audience at Oxford, İstanbul, and Ankara, and to Julian Bradfield, Aravind Joshi, Simon Kirby, Vincent Müller, Umut Özge, Geoffrey Pullum, Aaron Sloman, Mark Steedman, and Language Evolution and Computation Research Unit (LEC) at Edinburgh University, for comments and advice. I am to blame for all errors and for not heeding good advice. This research is supported by the GRAMPLUS project granted to Edinburgh University, EU FP7 Grant #249520.
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Bozşahin, C. (2016). Natural Recursion Doesn’t Work That Way: Automata in Planning and Syntax. In: Müller, V.C. (eds) Fundamental Issues of Artificial Intelligence. Synthese Library, vol 376. Springer, Cham. https://doi.org/10.1007/978-3-319-26485-1_7
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