Quantifiers satisfying semantic universals are simpler

Despite wide variation among natural languages, there are linguistic properties thought to be universal to all or almost all natural languages. Here, we consider universals at the semantic level, in the domain of quantifiers, which are given by the properties of monotonicity, quantity, and conservativity. We investigate whether these universals might be explained by differences in complexity. We generate a large collection of quantifiers, based on a simple yet expressive grammar, and compute both their complexities and whether they adhere to these universal properties. We find that quantifiers satisfying semantic universals are less complex: they have a shorter minimal description length.

Mental compression of binary sequences in a language of thought

The capacity to store information in working memory strongly depends upon the ability to recode the information in a compressed form. Here, we tested the theory that human adults encode binary sequences of stimuli in memory using a recursive compression algorithm akin to a “language of thought”, and capable of capturing nested patterns of repetitions and alternations. In five experiments, we probed memory for auditory or visual sequences using both subjective and objective measures. We used a sequence violation paradigm in which participants detected occasional violations in an otherwise fixed sequence. Both subjective ratings of complexity and objective sequence violation detection rates were well predicted by complexity, as measured by minimal description length (also known as Kolmogorov complexity) in the binary version of the “language of geometry”, a formal language previously found to account for the human encoding of complex spatial sequences in the proposed language. We contrasted the language model with a model based solely on surprise given the stimulus transition probabilities. While both models accounted for variance in the data, the language model dominated over the transition probability model for long sequences (with a number of elements far exceeding the limits of working memory). We use model comparison to show that the minimal description length in a recursive language provides a better fit than a variety of previous encoding models for sequences. The data support the hypothesis that, beyond the extraction of statistical knowledge, human sequence coding relies on an internal compression using language-like nested structures.

DESCRIPTIONAL COMPLEXITY IN ENCODED BLUM STATIC COMPLEXITY SPACES

Algorithmic Information Theory is based on the notion of descriptional complexity known as Chaitin-Kolmogorov complexity, defined in the '60s in terms of minimal description length. Blum Static Complexity spaces defined using Blum axioms, and Encoded Function spaces defined using properties of the complexity function, were introduced in 2012 to generalize the concept of descriptional complexity. In formal language theory we also use the concept of descriptional complexity for the number of states, or the number of transitions in a minimal finite automaton accepting a regular language, and apparently, this number has no connection to the general case of descriptional complexity. In this paper we prove that all the definitions of descriptional complexity, including complexity of operations, can be defined within the framework of Encoded Blum Static Complexity spaces, which extend both Blum Static Complexity spaces and Encoded Function spaces.

Hierarchical Modularity: Decomposition of Function Structures With the Minimal Description Length Principle

In engineering design and analysis, complex systems often need to be decomposed into a hierarchical combination of different simple subsystems. It’s necessary to provide formal, computable methods to hierarchically decompose complex structures. Since graph structures are commonly used as modeling methods in engineering practice, this paper presents a method to hierarchically decompose graph structures. The Minimal Description Length (MDL) principle is introduced as a measure to compare different decompositions. The best hierarchical decomposition is searched by evolutionary computation methods with newly defined crossover and mutation operators of tree structures. The results on abstract graph without attributes and a real function structure show that the technique is promising.