Concept learning becomes possible only when existing representations fail to account for experience. Most models of learning and inference, however, presuppose a fixed representational basis within which belief updating occurs. In this paper, I address a prior question: under what structural conditions can the representational basis itself expand in a principled and selective way? I propose a geometric framework in which conceptual growth is modeled as admissible basis extension evaluated under a Minimum Description Length (MDL) criterion. Experience, whether externally observed (...) or internally simulated, is represented as vectors relative to a current conceptual subspace. Residual components capture systematic representational failure, and candidate conceptual extensions are restricted to low-rank, admissible transformations. I show that any MDL-accepted extension can be chosen so that its novel directions lie entirely within the residual span induced by experience, while extensions orthogonal to this span strictly increase description length and are therefore rejected. This yields a conservative account of imagination and conceptual innovation. Internally generated counterfactual representations contribute to learning only insofar as they expose or amplify structured residual error, and cannot introduce arbitrary novelty. I further distinguish representational counterfactuals--counterfactuals over an agent's conceptual basis--from causal or value-level counterfactuals, and show how MDL provides a normative selection principle governing representational change. Overall, the framework characterizes conceptual development as an error-driven, geometry-constrained process of basis extension, clarifying both the role and the limits of imagination in learning and theory change. (shrink)

This paper presents a computational model of the way humans inductively identify and aggregate concepts from the low-level stimuli they are exposed to. Based on the idea that humans tend to select the simplest structures, it implements a dynamic hierarchical chunking mechanism in which the decision whether to create a new chunk is based on an information-theoretic criterion, the Minimum Description Length (MDL) principle. We present theoretical justifications for this approach together with results of an experiment in which participants, exposed (...) to meaningless symbols, have been implicitly encouraged to create high-level concepts by grouping them. Results show that the designed model, called hereafter MDLChunker, makes precise quantitative predictions both on the kind of chunks created by the participants and also on the moment at which these creations occur. They suggest that the simplicity principle used to design MDLChunker is particularly efficient to model chunking mechanisms. The main interest of this model over existing ones is that it does not require any adjustable parameter. (shrink)

The assembly of products or components by operators in industries is a complex task with recurring problems. In these processes, operators often make errors that can lead to defective products. Therefore, they need to be inspected later to verify their correct assembly. The main problems are caused by several reasons including high employee turnover, lack of experience in manufacturing specific products or confusion in interpreting instructions to assemble similar components. In this paper, a novel structured language aimed to describe the (...) required actions to manufacture a product in industrial assembly environments is presented. The main contribution is to provide a formal language to feed automatic systems that can verify through visual control whether the actions performed by the operator are carried out following the standard described by this language. In general, the use of this formal language will allow to minimize the negative impact of errors during assembly and to reduce waste in many forms in the industry. (shrink)

The Minimum Description Length principle is the modernformalisation of Occam's razor. It has been extensively and successfullyused in machine learning, especially for noisy and long sources ofdata. However, the MDL principle presents some paradoxes andinconveniences. After discussing all these, we address two of the mostrelevant: lack of explanation and lack of creativity. We present newalternatives to address these problems. The first one, intensionalcomplexity, avoids extensional parts in a description, so distributingcompression ratio in a more even way than the MDL principle. (...) The secondone, information gain, forces that the hypothesis is informative wrt. the evidence, so giving a formaldefinition of what is to discover. (shrink)

A decision tree is one of the machine learning techniques and also one of the major knowledge representations of data mining results.This is because it is easy to understand its meaning for human analysts.Even ID3, the representative algorithm, is known to exhibit remarkable performance deterioration under certain circumstances, particularly due to strong correlation between attributes representing the class of examples. One of the approaches to get more preferable decision trees is pre-processing the training data to extend its description, such as (...) attributes generation and attribute selection. There is also the idea of decision trees with a region rule. In this paper, we consider two approaches, i.e., decision trees with a region rule allowing multiple attributes, and a pre-processing method of a region rule to enabling any suitable number of attributes to correspond to branch nodes, where an optimal division condition with arbitrarily multiple attributes is acquired. By using this method, we propose a new decision tree generation algorithm guaranteeing to select effective compound attributes with each branch node, where an MDL-based new evaluation criterion is also defined for determining the optimal number of compound attributes specified to each node.This algorithm is applied to datasets containing only nominal values. It consists of three processes: compound attributes selection, parent node integration, and pruning. We call this new decision trees DTMACC (Decision Trees with Multiple Attributes Concept Clustering). The effectiveness and comprehensiveness of the proposed algorithm are confirmed through experiments comparing to the ordinary decision trees and an effective pre-processing method. (shrink)

This work empirically demonstrates a single dynamical law $ \mathcal{T} $ governing both neural (EEG) and physical (pendulum) systems, supporting the thesis that reality is a literal, computable machine. Using vector autoregression (VAR(2)), a shared second-order model compresses five diverse EEG environments (BIC = 1466.42) better than environment-specific alternatives (BIC = 1817.34; Δ ≈ 350), despite minor predictive loss. The law exhibits coefficient invariance, time-reversal symmetry, and induces a conserved process density $ \mu(t+1) - \mu(t) = 0 \pm \kappa $, (...) implying continuity of existence—no true cessation. We introduce recognition diagnostics (RI ≥ 0.8, CI ≤ 0.2) to quantify self-alignment with $ \mathcal{T} $—a measurable signature of intelligence as reflexive infinity ($ \mathcal{T}(\mathcal{T}(x)) = x' $). These results satisfy constructive (model fit) and exclusive (MDL superiority) proof criteria for a universal machine. Implications span philosophy of mind, metaphysics, and computational neuroscience: consciousness is conserved; death is transformation. Keywords: consciousness, transformation, continuity, machine realism, empirical metaphysics, dynamical systems, EEG, universal law. (shrink)

Natural language is full of patterns that appear to fit with general linguistic rules but are ungrammatical. There has been much debate over how children acquire these “linguistic restrictions,” and whether innate language knowledge is needed. Recently, it has been shown that restrictions in language can be learned asymptotically via probabilistic inference using the minimum description length (MDL) principle. Here, we extend the MDL approach to give a simple and practical methodology for estimating how much linguistic data are required to (...) learn a particular linguistic restriction. Our method provides a new research tool, allowing arguments about natural language learnability to be made explicit and quantified for the first time. We apply this method to a range of classic puzzles in language acquisition. We find some linguistic rules appear easily statistically learnable from language experience only, whereas others appear to require additional learning mechanisms (e.g., additional cues or innate constraints). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:66 Discussion REJOINDER TO DEJNOZKA'S REPLY GARY OSTERTAG Philosophy/ New YorkU. New York,NY 10003, USA [email protected] It is common knowledge that Russell does not explicitly endorse modal logic in any of his major logical writings. Nor does my review of BertrandRusseli onModalityand LogicalRelevance' suggest that Jan Dejnozka denies or is somehow unaware of this. On the contrary, I assume it to be obvious that any commitment Russell may have (...) had to modal logic must be implicitin his writings, nor explicit. The real issue is whether there is evidence of any such commitment. I will state, briefly,why I remain sceptical. First, Dejnozka's book lacks any interpretive methodology. When the question arises, In whichcontextsis itpermissibleto translateRusseli's language(formal orinformal)intoa modalsystem?, we get the following: amibute a modal logic to Russell if "it is more reasonable than not to paraphrase Russell's thinking into the modal logic." This condition, we are told, "is met to the extent that acertain modal logic is logicallyimplicit in Russell's thinking." All of which goes without saying, but it simply delays the inevitable question: when is a modal logic logicallyimplicit in a text? Dejnozka's current answer: a modal logic is logically implicit in a text when the text logically implies the paraphrase.2 But the final suggestion is incoherent, since we cannot tell what a text logical1y implies until we have discerned its logicalform-i.e. until we havealready paraphrased it into some formal idiom or other. A related problem is that Dejnozka consistently failsto distinguish two sorts of claims: • Certain passagesin Russell lend themselves to a modal interpretationthey can be captured in a given system of modal logic, e.g. S13. • Such an interpretation reflects Russell'sintentions. That a modal system captures one or another of Russell's accounts of logical truth in itself entails nothing regarding Russell'sintentions. The modal system G described by George Boolos in a munber of publications provides an alterna- ' "Russell's Modal Logic?", Russelin.s. 20 (2000): 165-72. 2 "Reply to Ostertag", Russell, n.s. 21 (2001): 63-5 (at 65). Discussion 67 rive formalization of Peano Arithmetic, enabling the derivation of Godel's incompleteness theorems. Yet the fact that this is possible does not in any way suggest that Godel himself was implicitly committed to G. Unfortunately, Dejnozka often writes as if the mere possibility of a modal interpretation is genuinely revealing as to Russell's intemions. Bm it is just as implausible to maintain this as it is to claim that it was Gi:idel'sintention to present Boolos's G.3 Second, as I maintain in my review, Dejnozka fails to take seriously the many comexts in which Russell is explicitly critical of modality. Dejnozka responds that he has quoted these very passagesand that he "embraces them as half-but only half-of [his] basic message" ("Reply", p. 64). But citing contexts in which Russell appears to find modality congenial does nothing to mitigate the force of the contexts in which Russell explicitly repudiates modality. It is Dejnozka's responsibility to explain how the latter are to cohere with his interpretation. To avoid this issue is to skirt the real philosophical and interpretive challenge that the project entails. Finally, we come to Dejnozka's confusions surrounding MDL-the triad of equivalences that underwrite the interpretation of Principiaas a modal logic. In light of Dejnozka's steadfast refusal to formalize the various modal systems he amibmes to Russell, it hardly makes a differencewhether MDLis a modal logic or merely, to use his terminology, a "modal theory" (assuming that the latter ultimately amounts to something other than a modal logic).4What is importam is whether MDLis trivial. If it is, then it is quite beside the point to pursue the various extensions of MDL.Since I maimain that Russell is not commined, implicitly or otherwise, to a substantive reading of MDL-one in which the modal operators have their conventional meanings-then he is not committed to these extensions, so there is no need for detailed discussion. What remains central is my argtunent for the claim that MDL is trivial. Bm this argmnent (unacknowledged by Dejnozka) is there for... (shrink)

Most accounts of consciousness begin by assuming the existence of a persisting subject and proceed to characterize what that subject experiences. This ordering creates a structural problem: the conditions under which a subject exists in the first place remain unspecified. We present a formal architecture in which identity is prior, consciousness is derived, and the relationship between them is governed by a self-consistency condition that existing frameworks do not possess. The architecture proceeds from seed-field to generative kernel, from kernel-equivalence quotient (...) to constraint manifold, from maintenance cost functional to viable region, and from viable region to regime stratification under substrate accessibility restriction. The key result is that the constraint manifold is not a static geometric object: it exists only for as long as recursive dynamics maintain the kernel whose equivalence class defines it. Consciousness is the high-coherence attractor state of those same dynamics, not an additional phenomenon requiring separate explanation. The formalism generates a precise, empirically testable prediction about anesthesia: consciousness loss need not involve a trajectory exiting the viable region. It can consist in the accessibility boundary sweeping inward across an occupied point while identity persists. This dissociation between identity and consciousness, and the geometric conditions under which it occurs, constitutes the primary empirical claim of the paper. (shrink)

We present a minimum message length (MML) framework for trajectory partitioning by point selection, and use it to automatically select the tolerance parameter ε for Douglas-Peucker partitioning, adapting to local trajectory complexity. By examining a range of ε for synthetic and real trajectories, it is easy to see that the best ε does vary by trajectory, and that the MML encoding makes sensible choices and is robust against Gaussian noise. We use it to explore the identification of micro-activities within a (...) longer trajectory. This MML metric is comparable to the TRACLUS metric – and shares the constraint of abstracting only by omission of points – but is a true lossless encoding. Such encoding has several theoretical advantages – particularly with very small segments (high frame rates) – but actual performance interacts strongly with the search algorithm. Both differ from unconstrained piecewise linear approximations, including other MML formulations. (shrink)