Statistical Default Logic (SDL) is an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, e.g., hypothesis testing and the estimation of a population‘s mean, variance and proportions. This paper presents an embedding of an important subset of SDL theories, called literal statistical default theories, into stable model semantics. The embedding is designed to compute the signature set of literals that uniquely (...) distinguishes each extension on a statistical default theory at a pre-assigned error-bound probability. (shrink)

In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, there (...) was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level. (shrink)

Reasoning by default is a relevant aspect of everyday life that has traditionally attracted the attention of many fields of research, from psychology to the philosophy of logic, from economics to artificial intelligence. Also in the field of law, default reasoning is widely used by lawyers, judges and other legal decision-makers. In this paper, a philosopher of language (Carlo Penco) and a philosopher of law (Damiano Canale) attempt to explore some uses of default reasoning that are scarcely (...) considered by legal theory. In particular, the dialogue dwells on the notion of literal meaning, witness testimony, and the problem of disagreement among experts in legal proceedings. The paper is intended as a sort of brain storming useful to identify new lines of research straddling philosophy of law, cognitive psychology and philosophy of language. (shrink)

Consider a gas that is adiabatically isolated from its environment and confined to the left half of a container. Then remove the wall separating the two parts. The gas will immediately start spreading and soon be evenly distributed over the entire available space. The gas has approached equilibrium. Thermodynamics (TD) characterizes this process in terms of an increase of thermodynamic entropy, which attains its maximum value at equilibrium. The second law of thermodynamics captures the irreversibility of this process by positing (...) that in an isolated system such as the gas entropy cannot decrease. The aim of statistical mechanics (SM) is to explain the behavior of the gas and, in particular, its conformity with the second law in terms of the dynamical laws governing the individual molecules of which the gas is made up. In what follows these laws are assumed to be the ones of Hamiltonian classical mechanics. We should not, however, ask for an explanation of the second law literally construed. This law is a universal law and as such cannot be explained by a statistical theory. But this is not a problem because we.. (shrink)

The aim of the paper is to determine how salient and non-salient figurative discourse nouns affect readers’ default response processing and oculo-graphic (eye-movement) reactions. Whereas the theories of the Graded Salience and the Defaultness Hypotheses, developed by R. Giora (Giora, 1999, 2003; Giora, Givoni, & Fein, 2015), have stimulated further research in the area of interpretive salience (Giora et al., 2015; Giora, Jaffe, Becker & Fein, 2018), the resonating influence of syntactic salience on default interpretations has been (...) largely neglected. In this study we provide corpus-based evidence followed by eye-tracking experiment verification, supportive of the synchronized influence of syntactic and lexical salience. The results show that default figurative responses in lexically salient positions may require more cognitive effort (longer fixations) if they are syntactically less salient. Literal responses to figurative nouns may also result from either weak lexical or syntactic salience of nouns. Therefore, apart from exemplifying resonance with lexical salience (in terms of lexical frequency, familiarity, conventionality, and prototypicality), the default figurative interpretations are also syntactically dependent. (shrink)

The default theory of aesthetic value combines hedonism about aesthetic value with strict perceptual formalism about aesthetic value, holding the aesthetic value of an object to be the value it has in virtue of the pleasure it gives strictly in virtue of its perceptual properties. A standard theory of aesthetic value is any theory of aesthetic value that takes the default theory as its theoretical point of departure. This paper argues that standard theories fail because they theorize (...) from the default theory. (shrink)

Cognitive functions are directly related to interactions between the brain's functional networks. This functional organization changes in the autism spectrum disorder (ASD). However, the heterogeneous nature of autism brings inconsistency in the findings, and specific pattern of changes based on the cognitive theories of ASD still requires to be well-understood. In this study, we hypothesized that the theory of mind (ToM), and the weak central coherence theory must follow an alteration pattern in the network level of functional interactions. The (...) main aim is to understand this pattern by evaluating interactions between all the brain functional networks. Moreover, the association between the significantly altered interactions and cognitive dysfunctions in autism is also investigated. We used resting-state fMRI data of 106 subjects (5–14 years, 46 ASD: five female, 60 HC: 18 female) to define the brain functional networks. Functional networks were calculated by applying four parcellation masks and their interactions were estimated using Pearson's correlation between pairs of them. Subsequently, for each mask, a graph was formed based on the connectome of interactions. Then, the local and global parameters of the graph were calculated. Finally, statistical analysis was performed using a two-sample t-test to highlight the significant differences between autistic and healthy control groups. Our corrected results show significant changes in the interaction of default mode, sensorimotor, visuospatial, visual, and language networks with other functional networks that can support the main cognitive theories of autism. We hope this finding sheds light on a better understanding of the neural underpinning of autism. (shrink)

It is shown here that the microcanonical ensemble for a system of noninteracting bosons and fermions contains a subensemble of state vectors for which all particles of the system are distinguishable. This “IQC” (inner quantum-classical) subensemble is therefore fully classical, except for a rather extreme quantization of particle momentum and position, which appears as the natural price that must be paid for distinguishability. The contribution of the IQC subensemble to the entropy is readily calculated, and the criterion for this to (...) be a good approximation to the exact entropy is a logarithmically strengthened form of the usual criterion for the validity of classical statistics in terms of the thermal de Broglie wavelength and the average volume per particle. Thus, it becomes possible to derive the Maxwell-Boltzmann distribution directly from the ensemble in the classical limit, using fully classical reasoning about the distinguishability of particles. The entropy is additive—theN! factor of the Boltzmann count cancels out in the course of the calculation, and the “N! paradox” is thereby resolved. The method of “correct Boltzmann counting” and the lowest term of the Wigner-Kirkwood series for the partition function are seen to be partly based on the IQC subensemble, and their partly nonclassical nature is clarified. The clear separation in the full ensemble of classical and nonclassical components makes it possible to derive the classical statistics of indistinguishable particles from their quantum statistics in a controlled, explicit way. This is particularly important for nonequilibrium theory. The treatment of molecular collisions along too-literally classical lines turns out to require exorbitantly high temperatures, although there are suggestions of indirect ways in which classical nonequilibrium theory might be justified at ordinary temperatures. The applicability of exact classical ergodic and mixing theory to systems at ordinary temperatures is called into question, although the general idea of coarse-graining is confirmed. The concepts on which the IQC idea is based are shown to give rise to a series development of thermostatistical quantities, starting with the distinguishable-particle approximation. (shrink)

Based on Newton’s laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed universe oscillating in phase-space. We find that the behavior of this universe as a whole can be represented by a free entropic oscillator whose lifespan is nonhomogeneous, thus implying that time is shorter or longer according to the state of this universe given through its entropy. We conclude that time reduces to the entropy (...) production of this universe and that a nonzero entropy production means that local fluctuations could exist giving rise to the appearance of masses and to the curvature of the space. (shrink)

Reports on beliefs, desires, and other attitudes continue to raise foundational questions about linguistic meaning and the pragmatics of utterance interpretation. There is a strong intuition that an attitude report like ‘John believes that Mary smokes’ can simply convey the singular proposition that the individual Mary is believed by John to have the property of smoking. Yet, there is also a strong intuition that ‘Lois believes that Superman can fly’ can additionally convey how an individual is represented . Cases of (...) this sort can be generated with any name in a suitable context . It is far from settled how this should be explained. I propose the Open Instruction Theory , according to which the linguistic meaning of attitude report sentences consists in instructions to create mental models, where those instructions leave open, depending on the state of the discourse, the possibility of singular interpretations as well as of complex interpretations including information about ways of representing. The account makes precise the idea that attitude report sentences with proper names are semantically nonspecific , rather than indexical , yielding predictions about syntactic constraints on interpretation. On this view, linguistic meaning itself does not provide determinate propositions. Since Gricean pragmatics requires determinate propositions as input, I propose new principles of pragmatics for literal utterance interpretation that do not require them but remain strongly constrained by linguistic meaning. The core principle is “inference to the most responsive interpretation.” Roughly, among the range of literal interpretations allowed by linguistic meaning, the listener generates the one that most fully answers the background question she seeks to answer by engaging in discourse. The pragmatics of literal utterance interpretation is the pragmatics of interpreting potential answers, even if communicative intention may be more important for conversational implicature. The account predicts cases in which our interpretations differ from what we would take the speaker to have had in mind. Singular interpretations of attitude reports have a special status as default interpretations. I suggest some advantages of OIT over indexicalist, DRT, and free enrichment theories. I argue that to the extent that we have to go beyond a strict principle of linguistic constraint , we should aim toward a principle of psychological constraint. (shrink)

Using a parallel with stage magic, it is argued that far from being seen as an extreme alternative, illusionism as articulated by Frankish should be considered the front runner, a conservative theory to be developed in detail, and abandoned only if it demonstrably fails to account for phenomena, not prematurely dismissed as 'counterintuitive'. We should explore the mundane possibilities thoroughly before investing in any magical hypotheses.

Statistical Learning Theory (e.g., Hastie et al., 2001; Vapnik, 1998, 2000, 2006) is the basic theory behind contemporary machine learning and data-mining. We suggest that the theory provides an excellent framework for philosophical thinking about inductive inference.

In this article, we provide a tutorial overview of some aspects of statistical learning theory, which also goes by other names such as statistical pattern recognition, nonparametric classification and estimation, and supervised learning. We focus on the problem of two-class pattern classification for various reasons. This problem is rich enough to capture many of the interesting aspects that are present in the cases of more than two classes and in the problem of estimation, and many of the results (...) can be extended to these cases. Focusing on two-class pattern classification simplifies our discussion, and yet it is directly applicable to a wide range of practical settings. (shrink)

We compare Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory . Popper’s notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.

A naturalistic scheme of primitive conceptual representations is proposed using the statistical measure of mutual information. It is argued that a concept represents, not the class of objects that caused its tokening, but the class of objects that is most likely to have caused it (had it been tokened), as specified by the statistical measure of mutual information. This solves the problem of misrepresentation which plagues causal accounts, by taking the representation relation to be determined via ordinal relationships (...) between conditional probabilities. The scheme can deal with statistical biases and does not rely on arbitrary criteria. Implications for the theory of meaning and semantic content are addressed. (shrink)

Most of the work in default logic is about default theories that are completely specified. In this category are the proposals of appropriate semantics for default logic, the characterizations of the complexity of reasoning with a default theory, the algorithms for finding consequences of default theories, etc. Relatively little attention has been paid to the process of building a default theory, and most of the work on this topic is about translating knowledge (...) bases from other formalisms (such as circumscription, autoepistemic logic, and action description languages) into default logic. This paper is about expressing knowledge in default logic. In particular, we assume that defaults are initially formulated as normal, and are then corrected using specific inference examples. (shrink)

A naturalistic scheme of primitive conceptual representations is proposed using the statistical measure of mutual information. It is argued that a concept represents, not the class of objects that caused its tokening, but the class of objects that is most likely to have caused it (had it been tokened), as specified by the statistical measure of mutual information. This solves the problem of misrepresentation which plagues causal accounts, by taking the representation relation to be determined via ordinal relationships (...) between conditional probabilities. The scheme can deal with statistical biases and does not rely on arbitrary criteria. Implications for the theory of meaning and semantic content are addressed. (shrink)

Default logic is computationally expensive. One of the most promising ways of easing this problem and developing powerful implementations is to split a default theory into smaller parts and compute extensions in a modular, local way. This paper compares two recent approaches, Turner's splitting and Cholewinski's stratification. It shows that the approaches are closely related – in fact the former can be viewed as a special case of the latter.

In _Reliable Reasoning_, Gilbert Harman and Sanjeev Kulkarni -- a philosopher and an engineer -- argue that philosophy and cognitive science can benefit from statistical learning theory, the theory that lies behind recent advances in machine learning. The philosophical problem of induction, for example, is in part about the reliability of inductive reasoning, where the reliability of a method is measured by its statistically expected percentage of errors -- a central topic in SLT. After discussing philosophical attempts to evade (...) the problem of induction, Harman and Kulkarni provide an admirably clear account of the basic framework of SLT and its implications for inductive reasoning. They explain the Vapnik-Chervonenkis dimension of a set of hypotheses and distinguish two kinds of inductive reasoning. The authors discuss various topics in machine learning, including nearest-neighbor methods, neural networks, and support vector machines. Finally, they describe transductive reasoning and suggest possible new models of human reasoning suggested by developments in SLT. (shrink)

Grice's distinction between what is said by a sentence and what is implicated by an utterance of it is both extremely familiar and almost universally accepted. However, in recent literature, the precise account he offered of implicature recovery has been questioned and alternative accounts have emerged. In this paper, I examine three such alternative accounts. My main aim is to show that the two most popular accounts in the current literature still face signifi cant problems. I will then conclude by (...) suggesting that an alternative account, emerging from semantic minimalism, is best placed to accommodate Grice's distinction. (shrink)

The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) classical random field. Quantum averages can (...) be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger’s equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The “effect of entanglement” is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein. (shrink)

Nelson Goodman's new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper's notion of degrees of testability is linked (...) to minimizing expected predictive error. In contrast, formal learning theory appeals to Ockham's razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth. In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result for a class of inductive problems that I call strongly VC ordered, of which Goodman's riddle is just one example. (shrink)

The idea that “simplicity is a sign of truth”, and the related “Occam’s razor” principle, stating that, all other things being equal, simpler models should be preferred to more complex ones, have been long discussed in philosophy and science. We explore these ideas in the context of supervised machine learning, namely the branch of artificial intelligence that studies algorithms which balance simplicity and accuracy in order to effectively learn about the features of the underlying domain. Focusing on statistical learning (...) theory, we show that situations exist for which a preference for simpler models provably slows down, instead of favoring, the supervised learning process. Our results shed new light on the relations between simplicity and truth approximation, which are briefly discussed in the context of both machine learning and the philosophy of science. (shrink)

In Salmon's discussion of his account of statistical relevance and statistical explanation there is a peculiarity in the selection of examples. Where he wishes to show that statistical accounts are reasonably treated as explanatory, he draws examples from the social sciences, such as juvenile delinquency. But when he explains the concept of 'causal' relevance, the examples are selected from the natural sciences. This conceals difficulties with salmon's account of causality in the face of multiple causes such as (...) are characteristic of the social sciences. Salmon's account is shown not to escape difficulties associated with Simon's earlier approach. (shrink)

This essay demonstrates a previously unnoticed connection between formal and statistical learning theory with regard to Nelson Goodman’s new riddle of induction. Discussions of Goodman’s riddle in formal learning theory explain how conjecturing “all green” before “all grue” can enhance efficient convergence to the truth, where efficiency is understood in terms of minimizing the maximum number of retractions or “mind changes.” Vapnik-Chervonenkis (VC) dimension is a central concept in statistical learning theory and is similar to Popper’s notion of (...) degrees of testability. I show that for a class inductive problems of which Goodman’s riddle is one example, a reliable inductive method minimizes the maximum number of mind changes exactly if it always conjectures the hypothesis from the set with lowest VC dimension consistent with the data. I also discuss the relevance of these results to language invariance and curve fitting. (shrink)

In this paper, I show that Polleit and Mariano (2011) are right in concluding that Credit Default Swaps (CDS) are per se unobjectionable from Rothbard’s libertarian perspective on property rights and contract theory, but that they fail to derive this conclusion properly. I therefore outline the proper explanation. In addition, though Polleit and Mariano are correct in pointing out that speculation with CDS can conceivably hurt the borrowers’ interests, they fail to grasp that this can be the case only (...) in some peculiar circumstances that I identify. In other words, they miss the bigger picture, the one outside special circumstances, in which CDS trading has the opposite effect. That is, CDS facilitate debt accumulation, including government debt accumulation. Finally, I point out how this can precipitate the collapse of fiat money regimes. An incidental goal of the analysis is to provide a better account than Polleit and Mariano of recent government interventions in and around CDS markets. (shrink)

Nelson Goodman’s new riddle of induction forcefully illustrates a challenge that must be confronted by any adequate theory of inductive inference: provide some basis for choosing among alternative hypotheses that fit past data but make divergent predictions. One response to this challenge is to distinguish among alternatives by means of some epistemically significant characteristic beyond fit with the data. Statistical learning theory takes this approach by showing how a concept similar to Popper’s notion of degrees of testability is linked (...) to minimizing expected predictive error. In contrast, formal learning theory appeals to Ockham’s razor, which it justifies by reference to the goal of enhancing efficient convergence to the truth. In this essay, I show that, despite their differences, statistical and formal learning theory yield precisely the same result for a class of inductive problems that I call strongly VC ordered , of which Goodman’s riddle is just one example. (shrink)

Currently there is hardly any connection between philosophy of science and Artificial Intelligence research. We argue that both fields can benefit from each other. As an example of this mutual benefit we discuss the relation between Inductive-Statistical Reasoning and Default Logic. One of the main topics in AI research is the study of common-sense reasoning with incomplete information. Default logic is especially developed to formalise this type of reasoning. We show that there is a striking resemblance between (...) inductive-statistical reasoning and default logic. A central theme in the logical positivist study of inductive-statistical reasoning such as Hempels Criterion of Maximal Specificity turns out to be equally important in default logic. We also discuss to what extent the relevance of the results of Logical Positivism to AI research could contribute to a reevaluation of Logical Positivism in general. (shrink)