Where does a probabilistic language-of-thought (PLoT) come from? How can we learn new concepts based on probabilistic inferences operating on a PLoT? Here, I explore these questions, sketching a traditional circularity objection to LoT and canvassing various approaches to addressing it. I conclude that PLoT-based cognitive architectures can support genuine concept learning; but, currently, it is unclear that they enjoy more explanatory breadth in relation to concept learning than alternative architectures that do not posit any LoT.

The Intergovernmental Panel on Climate Change (IPCC) often qualifies its statements by use of probabilistic “likelihood” language. In this paper, I show that this language is not properly interpreted in either frequentist or Bayesian terms—simply put, the IPCC uses both kinds of statistics to calculate these likelihoods. I then offer a deflationist interpretation: the probabilistic language expresses nothing more than how compatible the evidence is with the given hypothesis according to some method that generates normalized scores. I end (...) by drawing some tentative normative conclusions. (shrink)

Using an asymptotic characterization of probabilistic finite state languages over a one-letter alphabet we construct a probabilistic language with regular support that cannot be generated by probabilistic CFGs. Since all probability values used in the example are rational, our work is immune to the criticism leveled by Suppes (Synthese 22:95–116, 1970 ) against the work of Ellis ( 1969 ) who first constructed probabilistic FSLs that admit no probabilistic FSGs. Some implications for probabilistic (...) language modeling by HMMs are discussed. (shrink)

This article provides an overview of a probabilistic constraints framework for thinking about language acquisition and processing. The generative approach attempts to characterize knowledge of language (i.e., competence grammar) and then asks how this knowledge is acquired and used. Our approach is performance oriented: the goal is to explain how people comprehend and produce utterances and how children acquire this skill. Use of language involves exploiting multiple probabilistic constraints over various types of linguistic and nonlinguistic information. Acquisition is (...) the process of accumulating this information, which begins in infancy. The constraint satisfaction processes that are central to language use are the same as the bootstrapping processes that provide entry to language for the child. Framing questions about acquisition in terms of models of adult performance unifies the two topics under a set of common principles and has important consequences for arguments concerning language learnability. (shrink)

Probabilistic methods are providing new explanatory approaches to fundamental cognitive science questions of how humans structure, process and acquire language. This review examines probabilistic models defined over traditional symbolic structures. Language comprehension and production involve probabilistic inference in such models; and acquisition involves choosing the best model, given innate constraints and linguistic and other input. Probabilistic models can account for the learning and processing of language, while maintaining the sophistication of symbolic models. A recent burgeoning of (...) theoretical developments and online corpus creation has enabled large models to be tested, revealing probabilistic constraints in processing, undermining acquisition arguments based on a perceived poverty of the stimulus, and suggesting fruitful links with probabilistic theories of categorization and ambiguity resolution in perception. (shrink)

Monogenesis of language is widely accepted, but the conventional argument seems to be mistaken; a simple probabilistic model shows that polygenesis is likely. Other prehistoric inventions are discussed, as are problems in tracing linguistic lineages. Language is a system of representations; within such a system, words can evoke complex and systematic responses. Along with its social functions, language is important to humans as a mental instrument. Indeed, the invention of language,that is the accumulation of symbols to represent emotions, objects, (...) and acts may be the most important event in human evolution, because so many developments follow from it. For example, Edward Sapir speculated that some embryonic form of language must have been available to early man to help him fashion tools from stone (Sapir,1921). Sophisticated biface stone tools date to early Homo erectus some 1.5 million years ago, suggesting a similar age for language. This paper considers whether the invention of language occurred at only one pre-historic site or at several sites. In other words, did language emerge by monogenesis or polygenesis? Early thinkers believed in monogenesis, against a background of divine creation. Perhaps the best known account is the biblical story of Adam giving names to plants and animals in the Garden of Eden. Similar legends are found among many peoples. Modern linguists too assume monogenesis, but on probabilistic grounds (see, for instance, Southworth and Daswani, 1974, p.314). The argument seems to be that the invention of language is an extremely unlikely event, because symbolization involves abstraction and requires synchronized insight by several individuals; therefore, the probability of occurrence at more than one site must be vanishingly small. We have found no explicit quantitative treatment of this question in the literature, but the underlying logic has to be the multiplication of probabilities. If p is small at one site,then p.p for two sites is smaller still, and so on. This reasoning is false, as we show here. The fallacy lies in the focus on two particular sites rather than consideration of all pairs of sites. (shrink)

In this article, I explain how a variant of David Miller's argument concerning the language dependence of the accuracy of predictions can be applied to Joyce's notion of the accuracy of “estimates of numerical truth-values”. This leads to a potential problem for Joyce's accuracy-dominance-based argument for the conclusion that credences should obey the probability calculus.

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)

We investigate an approach for drawing logical inference from inconsistent premisses. The main idea in this approach is that the inconsistencies in the premisses should be interpreted as uncertainty of the information. We propose a mechanism, based on Kinght’s [14] study of inconsistency, for revising an inconsistent set of premisses to a minimally uncertain, probabilistically consistent one. We will then generalise the probabilistic entailment relation introduced in [15] for propositional languages to the first order case to draw logical (...) inference from a probabilistic set of premisses. We will show how this combination can allow us to limit the effect of uncertainty introduced by inconsistent premisses to only the reasoning on the part of the premise set that is relevant to the inconsistency. (shrink)

It is argued that suitably trained neural language models exhibit key properties of epistemic agency: they hold probabilistically coherent and logically consistent degrees of belief, which they can rationally revise in the face of novel evidence. To this purpose, we conduct computational experiments with rankers: T5 models [Raffel et al. 2020] that are pretrained on carefully designed synthetic corpora. Moreover, we introduce a procedure for eliciting a model’s degrees of belief, and define numerical metrics that measure the extent to which (...) given degrees of belief violate (probabilistic, logical, and Bayesian) rationality constraints. While pretrained rankers are found to suffer from global inconsistency (in agreement with, e.g., [Jang et al. 2021]), we observe that subsequent self-training on auto-generated texts allows rankers to gradually obtain a probabilistically coherent belief system that is aligned with logical constraints. In addition, such self-training is found to have a pivotal role in rational evidential learning, too, for it seems to enable rankers to propagate a novel evidence item through their belief systems, successively re-adjusting individual degrees of belief. All this, we conclude, confirms the Rationality Hypothesis, i.e., the claim that suitable trained NLMs may exhibit advanced rational skills. We suggest that this hypothesis has empirical, yet also normative and conceptual ramifications far beyond the practical linguistic problems NLMs have originally been designed to solve. (shrink)

Ibeling et al. (2023) axiomatize increasingly expressive languages of causation and probability, and Mossé et al. (2024) show that reasoning (specifically the satisfiability problem) in each causal language is as difficult, from a computational complexity perspective, as reasoning in its merely probabilistic or “correlational” counterpart. Introducing a summation operator to capture common devices that appear in applications—such as the do-calculus of Pearl (2009) for causal inference, which makes ample use of marginalization—van der Zander et al. (2023) partially extend (...) these earlier complexity results to causal and probabilistic languages with marginalization. We complete this extension, fully characterizing the complexity of probabilistic and causal reasoning with summation, demonstrating that these again remain equally difficult. Surprisingly, allowing free variables for random variable values results in a system that is undecidable, so long as the ranges of these random variables are unrestricted. We finally axiomatize these languages featuring marginalization (or more generally summation), resolving open questions posed by Ibeling et al. (2023). (shrink)

Experimental research shows that human sentence processing uses information from different levels of linguistic analysis, for example, lexical and syntactic preferences as well as semantic plausibility. Existing computational models of human sentence processing, however, have focused primarily on lexico‐syntactic factors. Those models that do account for semantic plausibility effects lack a general model of human plausibility intuitions at the sentence level. Within a probabilistic framework, we propose a wide‐coverage model that both assigns thematic roles to verb–argument pairs and determines (...) a preferred interpretation by evaluating the plausibility of the resulting (verb, role, argument) triples. The model is trained on a corpus of role‐annotated language data. We also present a transparent integration of the semantic model with an incremental probabilistic parser. We demonstrate that both the semantic plausibility model and the combined syntax/semantics model predict judgment and reading time data from the experimental literature. (shrink)

We introduce a set of biologically and computationally motivated design choices for modeling the learning of language, or of other types of sequential, hierarchically structured experience and behavior, and describe an implemented system that conforms to these choices and is capable of unsupervised learning from raw natural-language corpora. Given a stream of linguistic input, our model incrementally learns a grammar that captures its statistical patterns, which can then be used to parse or generate new data. The grammar constructed in this (...) manner takes the form of a directed weighted graph, whose nodes are recursively (hierarchically) defined patterns over the elements of the input stream. We evaluated the model in seventeen experiments, grouped into five studies, which examined, respectively, (a) the generative ability of grammar learned from a corpus of natural language, (b) the characteristics of the learned representation, (c) sequence segmentation and chunking, (d) artificial grammar learning, and (e) certain types of structure dependence. The model's performance largely vindicates our design choices, suggesting that progress in modeling language acquisition can be made on a broad front—ranging from issues of generativity to the replication of human experimental findings—by bringing biological and computational considerations, as well as lessons from prior efforts, to bear on the modeling approach. (shrink)

Words are the essence of communication: They are the building blocks of any language. Learning the meaning of words is thus one of the most important aspects of language acquisition: Children must first learn words before they can combine them into complex utterances. Many theories have been developed to explain the impressive efficiency of young children in acquiring the vocabulary of their language, as well as the developmental patterns observed in the course of lexical acquisition. A major source of disagreement (...) among the different theories is whether children are equipped with special mechanisms and biases for word learning, or their general cognitive abilities are adequate for the task. We present a novel computational model of early word learning to shed light on the mechanisms that might be at work in this process. The model learns word meanings as probabilistic associations between words and semantic elements, using an incremental and probabilistic learning mechanism, and drawing only on general cognitive abilities. The results presented here demonstrate that much about word meanings can be learned from naturally occurring child-directed utterances (paired with meaning representations), without using any special biases or constraints, and without any explicit developmental changes in the underlying learning mechanism. Furthermore, our model provides explanations for the occasionally contradictory child experimental data, and offers predictions for the behavior of young word learners in novel situations. (shrink)

The paper offers a formalization of reasoning about distributed multi-agent systems. The presented propositional probabilistic temporal epistemic logic $\textbf {PTEL}$ is developed in full detail: syntax, semantics, soundness and strong completeness theorems. As an example, we prove consistency of the blockchain protocol with respect to the given set of axioms expressed in the formal language of the logic. We explain how to extend $\textbf {PTEL}$ to axiomatize the corresponding first-order logic.

While rules and exemplars are usually viewed as opposites, this paper argues that they form end points of the same distribution. By representing both rules and exemplars as (partial) trees, we can take into account the fluid middle ground between the two extremes. This insight is the starting point for a new theory of language learning that is based on the following idea: If a language learner does not know which phrase‐structure trees should be assigned to initial sentences, s/he allows (...) (implicitly) for all possible trees and lets linguistic experience decide which is the “best” tree for each sentence. The best tree is obtained by maximizing “structural analogy” between a sentence and previous sentences, which is formalized by the most probable shortest combination of subtrees from all trees of previous sentences. Corpus‐based experiments with this model on the Penn Treebank and the Childes database indicate that it can learn both exemplar‐based and rule‐based aspects of language, ranging from phrasal verbs to auxiliary fronting. By having learned the syntactic structures of sentences, we have also learned the grammar implicit in these structures, which can in turn be used to produce new sentences. We show that our model mimicks children’s language development from item‐based constructions to abstract constructions, and that the model can simulate some of the errors made by children in producing complex questions. (shrink)

Probabilistic models of sentence comprehension are increasingly relevant to questions concerning human language processing. However, such models are often limited to syntactic factors. This restriction is unrealistic in light of experimental results suggesting interactions between syntax and other forms of linguistic information in human sentence processing. To address this limitation, this article introduces two sentence processing models that augment a syntactic component with information about discourse co-reference. The novel combination of probabilistic syntactic components with co-reference classifiers permits them (...) to more closely mimic human behavior than existing models. The first model uses a deep model of linguistics, based in part on probabilistic logic, allowing it to make qualitative predictions on experimental data; the second model uses shallow processing to make quantitative predictions on a broad-coverage reading-time corpus. (shrink)

The question of whether humans represent grammatical knowledge as a binary condition on membership in a set of well-formed sentences, or as a probabilistic property has been the subject of debate among linguists, psychologists, and cognitive scientists for many decades. Acceptability judgments present a serious problem for both classical binary and probabilistic theories of grammaticality. These judgements are gradient in nature, and so cannot be directly accommodated in a binary formal grammar. However, it is also not possible to (...) simply reduce acceptability to probability. The acceptability of a sentence is not the same as the likelihood of its occurrence, which is, in part, determined by factors like sentence length and lexical frequency. In this paper, we present the results of a set of large-scale experiments using crowd-sourced acceptability judgments that demonstrate gradience to be a pervasive feature in acceptability judgments. We then show how one can predict acceptability judgments on the basis of probability by augmenting probabilistic language models with an acceptability measure. This is a function that normalizes probability values to eliminate the confounding factors of length and lexical frequency. We describe a sequence of modeling experiments with unsupervised language models drawn from state-of-the-art machine learning methods in natural language processing. Several of these models achieve very encouraging levels of accuracy in the acceptability prediction task, as measured by the correlation between the acceptability measure scores and mean human acceptability values. We consider the relevance of these results to the debate on the nature of grammatical competence, and we argue that they support the view that linguistic knowledge can be intrinsically probabilistic. (shrink)

This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, (...) and may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)

In this paper we systematically derive a predicate transformer semantics from a direct semantics for a simple probabilistic-nondeterministic programming language . This goal is achieved by exhibiting the direct semantics as isomorphic to a continuation semantics from which the predicate transformer semantics can be read off immediately. This isomorphism allows one to identify nonempty convex compact saturated sets of valuations on the set S of states with certain “good” functionals from to in a way similar to the one how (...) H. Minkowski in 1903 related nonempty convex compact subsets of to what is nowadays called Minkowski functionals. (shrink)

Traditional philosophical discussions of knowledge have focused on the epistemic status of full beliefs. In this book, Moss argues that in addition to full beliefs, credences can constitute knowledge. For instance, your .4 credence that it is raining outside can constitute knowledge, in just the same way that your full beliefs can. In addition, you can know that it might be raining, and that if it is raining then it is probably cloudy, where this knowledge is not knowledge of propositions, (...) but of probabilistic contents. -/- The notion of probabilistic content introduced in this book plays a central role not only in epistemology, but in the philosophy of mind and language as well. Just as tradition holds that you believe and assert propositions, you can believe and assert probabilistic contents. Accepting that we can believe, assert, and know probabilistic contents has significant consequences for many philosophical debates, including debates about the relationship between full belief and credence, the semantics of epistemic modals and conditionals, the contents of perceptual experience, peer disagreement, pragmatic encroachment, perceptual dogmatism, and transformative experience. In addition, accepting probabilistic knowledge can help us discredit negative evaluations of female speech, explain why merely statistical evidence is insufficient for legal proof, and identify epistemic norms violated by acts of racial profiling. Hence the central theses of this book not only help us better understand the nature of our own mental states, but also help us better understand the nature of our responsibilities to each other. (shrink)

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular (...) languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning. (shrink)

According to probabilistic theories of reasoning in psychology, people's degree of belief in an indicative conditional `if A, then B' is given by the conditional probability, P(B|A). The role of language pragmatics is relatively unexplored in the new probabilistic paradigm. We investigated how consequent relevance a ects participants' degrees of belief in conditionals about a randomly chosen card. The set of events referred to by the consequent was either a strict superset or a strict subset of the set (...) of events referred to by the antecedent. We manipulated whether the superset was expressed using a disjunction or a hypernym. We also manipulated the source of the dependency, whether in long-term memory or in the stimulus. For subset-consequent conditionals, patterns of responses were mostly conditional probability followed by conjunction. For superset-consequent conditionals, conditional probability responses were most common for hypernym dependencies and least common for disjunction dependencies, which were replaced with responses indicating inferred consequent irrelevance. Conditional probability responses were also more common for knowledge-based than stimulus-based dependencies. We suggest. (shrink)

This work is in two parts. The main aim of part 1 is a systematic examination of deductive, probabilistic, inductive and purely inductive dependence relations within the framework of Kolmogorov probability semantics. The main aim of part 2 is a systematic comparison of (in all) 20 different relations of probabilistic (in)dependence within the framework of Popper probability semantics (for Kolmogorov probability semantics does not allow such a comparison). Added to this comparison is an examination of (in all) 15 (...) purely inductive dependence relations. ————Part 1 leads in an axiomatic step-by-step development from the elementary classical truth value semantics of a sentential-logical language, called ‘L’, (chapter 1) to the elementary Kolmogorov probability semantics of L (chapter 2), which is then extended to four axiomatic semantical theories of dependence relations between the formulae of L. First the elementary Kolmogorov probability semantics of L is extended to a theory, called ‘Kdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 3). Then Kdd is extended to a theory, called ‘Kpd1’, of the degree to which formulae of L probabilistically depend on each other in regard to a given probability distribution on the set of all formulae of L (chapter 4). Kpd1, in its turn, gets extended to a theory, called ‘Kpd2’, of the relations of probabilistic dependence and independence, relativized to unary Kolmogorov probability functions defined on L (chapter 5). Then Kpd2 is extended to a theory, called ‘Kid’, of the relations of inductive dependence and inductive independence, again relativized to unary Kolmogorov probability functions defined on L (chapter 6). Finally, Kid is extended to a theory, called ‘Kpid’, of the relations of purely inductive positive and negative dependence, relativized to unary Kolmogorov probability functions defined on L (chapter 7). ——Chapter 1, which deals with the familiar notions of truth value functions, tautologies, consequence relations and relations of logical opposition, is naturally the shortest chapter of part 1.——In chapter 2, the elementary classical semantics of L is extended to the elementary Kolmogorov probability semantics of L, i.e. to an axiomatic theory of unary and of binary Kolmogorov probability functions defined on the set of formulae of L. Because of the elementary character of this theory, chapter 2 is also rather short.——Chapter 3 introduces the first theory on dependence relations, to wit: Kdd, the theory of deductive (in)dependence between formulae of L. I follow here the well-known idea of Popper and Miller, who have used it in a famous discussion on the nature of probabilistic support for their arguments that probabilistic support is deductive, not inductive. I develop Kdd in the form of about 100 theorems, making ample use of the fact that deductive independence is nothing but subcontrary opposition, and close with a remark on the fundamental difference between deductive and logical dependence—two relations the ideas of which are all too easily mixed up.——Chapters 4 and 5 deal extensively with the traditional ideas of probabilistic (in)dependence, applied to formulae rather than to events. As always, I proceed axiomatically in a step-by-step process under systematic viewpoints and obtain about 300 theorems in this way. In the formulation of the theorems, I took special care to state clearly and expressly so-called tacit assumptions, especially those concerning the probability values of the formulae said to be dependent on each other. These assumptions are usually missing in the literature, due either to economy of writing or to sloppiness of thinking. Presumably, both chapters contain little that is new, their value lying more in the systematic grouping and organic development of the theorems than in the newness of these.——In chapter 6, I extend the axiomatic theory about probabilistic (in)dependence which has been elaborated in chapter 5, to an axiomatic theory of inductive (in)dependence by requiring of the relation of inductive (in)dependence that it be probabilistic (in)dependence, but not also logical implication or logical opposition. I point out the differences between probabilistic and inductive (in)dependence by means of some 60 theorems and close my examination of inductive (in)dependence by considering its relationship to the notion of support in the philosophy of science.——Finally, in chapter 7, the last of part 1, I take the step from inductive dependence to what I call ‘purely inductive dependence’ by combining the idea of inductive dependence with that of deductive independence in a way which is suggested by writings of Popper and Miller. I arrive at two noteworthy theorems. Firstly, there is indeed no purely inductive support. But secondly, and perhaps amazingly, countersupport is purely inductive.————Whereas the probabilistic framework of part 1 of the present work is Kolmogorov probability semantics, the framework of part 2 is Popper probability semantics, which is not only worth examining as a fascinating alternative to orthodox Kolmogorov probability semantics, but also allows us to examine dependence relations more deeply, than Kolmogorov probability semantics does. Part 2 leads—again in an axiomatic step-by-step development—from the basic Popper probability semantics of L, called ‘Pb’, (chapter 8) via a probabilistic theory of logical attributes, called ‘Ps’, (chapter 9) to four axiomatic semantical theories of dependence relations between the formulae of L. First, Ps is extended to a theory, called ‘Pdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 10). Then Pdd is extended to a theory, called ‘Ppd’, of (in all) 20 relations of probabilistic (in)dependence, relativized to binary Popper probability functions defined on L (chapter 11). Ppd, in its turn, is extended to a theory, called ‘Pid’, of (in all) 10 relations of inductive dependence, again relativized to binary Popper probability functions defined on L (first part of chapter 12). Finally, Pid is extended to a theory, called ‘Ppid’, of (in all) 15 relations of purely inductive positive and negative dependence, relativized to binary Popper probability functions defined on L (second part of chapter 12).——Chapter 8, the first chapter of part 2 of the present work, is entirely preparatory. It introduces the axioms and about 180 theorems (150 of them together with their proofs) of basic Popper probability semantics in order to set this kind of semantics under way.——Then, in chapter 9, basic Popper probability semantics is extended to a probabilistic theory of logical properties of and relations between the formulae of L. Although I think that the way I did this extension is of some interest in itself, the main task of chapter 9 is again a preparatory one: to yield the indispensable lemmata (about 90 in number) for the theorems concerning probabilistic dependence relations in chapter 11 and concerning inductive dependence relations in chapter 12.——Chapter 10 brings the extension of Ps to the theory Pdd of deductive (in)dependence. Only half a dozen theorems are noted here for later use in the Pdd-extensions Ppd and Ppid. In view of the over 100 theorems already gained on this topic in the Kolmogorovian framework (cf. chapter 3), a similar extensive elaboration of Pdd would have been superfluous.——Chapter 11 is the most important one of part 2. It consists of a systematic comparison of 20 probabilistic (in)dependence concepts by means of about 230 theorems, obtained within the axiomatic theory Ppd, which is built up as an extension of Pdd. The main points of comparison were: differences in logical strength; reflexivity and symmetry; behaviour under the condition that the probability values of the formulae in question are extreme. It turned out that each of the examined concepts violates a strong and straightforward version of the intuitive requirement that probabilistic dependence should go with logical dependence. Whereas the corresponding chapter 5 in part 1 of the present work may not have led to new theorems, chapter 11 yields dozens of them in the process of comparison of concepts of dependence and independence which had—as far as I know—never before been treated in a single theoretical framework. With Popper probability semantics, this framework has become available, and here I have simply made full use of it.——In chapter 12, I extend the theory Ppd of probabilistic (in)dependence to the theories Pid and Ppid of inductive and purely inductive dependence, in a way very similar to that in which I have extended the theory Kpd2 to the theories Kid and Kpid in chapters 6 and 7. The first main result of Kpid (roughly: there is no purely inductive support) could be repeated for four of the five purely inductive positive dependence relations considered in chapter 12, whereas the second main result of Kpid (roughly: there is purely inductive countersupport ) could be repeated for each of the five examined purely inductive negative dependence relations. Chapter 12 closes with a brief recapitulation and critical discussion of the main results. (shrink)

A probabilistic and counterfactual theory of causality is developed within the framework of branching time. The theory combines ideas developed by James Fetzer, Donald Nute, Patrick Suppes, Ming Xu, John Pollock, David Lewis and Mellor among others.

The problems of access—retrieving linguistic structure from some mental grammar —and disambiguation—choosing among these structures to correctly parse ambiguous linguistic input—are fundamental to language understanding. The literature abounds with psychological results on lexical access, the access of idioms, syntactic rule access, parsing preferences, syntactic disambiguation, and the processing of garden‐path sentences. Unfortunately, it has been difficult to combine models which account for these results to build a general, uniform model of access and disambiguation at the lexical, idiomatic, and syntactic levels. (...) For example, psycholinguistic theories of lexical access and idiom access and parsing theories of syntactic rule access have almost no commonality in methodology or coverage of psycholinguistic data. This article presents a single probabilistic algorithm which models both the access and disambiguation of linguistic knowledge. The algorithm is based on a parallel parser which ranks constructions for access, and interpretations for disambiguation, by their conditional probability. Low‐ranked constructions and interpretations are pruned through beam‐search; this pruning accounts, among other things, for the garden‐path effect. I show that this motivated probabilistic treatment accounts for a wide variety of psycholinguistic results, arguing for a more uniform representation of linguistic knowledge and for the use of probabilistically‐enriched grammars and interpreters as models of human knowledge of and processing of language. (shrink)

Hans Reichenbach’s posthumous book The Direction of Time ends somewhere between Socratic aporia and historical irony. Prompted by Feynman’s diagrammatic formulation of quantum electrodynamics, Reichenbach eventually abandoned the delicate balancing between the macroscopic foundation of the direction of time and microscopic descriptions of time order undertaken throughout the previous chapters in favor of an exclusively macroscopic theory that he had vehemently rejected in the 1920s. I analyze Reichenbach’s reasoning against the backdrop of the history of Feynman diagrams and the current (...) practice of particle physics. Building upon the debates about processes and conserved quantities between Wesley Salmon and Phil Dowe in the 1990s, and the exchange between Reichenbach and the gestalt theorist Kurt Lewin during the 1920s about topology and genidentity, I investigate whether the aporia about local time order could be avoided by following a strategy that Reichenbach adopted elsewhere in the book and develop a notion of functional genidentity that captures the practice of present-day elementary particle physics and the fact that Feynman diagrams have to be understood in the context of a complex mathematical description of scattering processes. (shrink)

We show how to obtain a probabilistic semantics and calculus for a logic presented by a valuation specification. By identifying general forms of valuation constraints we are able to accommodate a wide class of propositional based logics encompassing multi-valued logics like Łukasiewicz 3-valued logic and the Belnap–Dunn four-valued logic as well as paraconsistent logics like $${\textsf{mbC}}$$ and $${\textsf{LFI1}}$$. The probabilistic calculus is automatically generated from the valuation specification. Although not having explicit probability constructors in the language, the rules (...) of the calculus reflect the valuation constraints in a probabilistic way. Indeed the probability of the premises of each rule coincides with the probability of the conclusions. Moreover, a failed exhaustive attempt of proving a formula in this calculus means non-derivability. Nevertheless when the non-derived formula is consistent then it is possible to extract a satisfying valuation from the failed exhaustive attempt. Soundness and completeness of the calculi are established with respect to the probabilistic semantics consisting of probability spaces also induced by the valuation specification. Furthermore we prove the equivalence between the probabilistic and the valuation semantics. (shrink)

The paper starts with the distinction between conjunction-of-parts accounts and disjunction-of-possibilities accounts to truthlikeness. In Sect. 3, three distinctions between kinds of truthlikeness measures are introduced: comparative versus numeric t-measures, t-measures for qualitative versus quantitative theories, and t-measures for deterministic versus probabilistic truth. These three kinds of truthlikeness are explicated and developed within a version of conjunctive part accounts based on content elements. The focus lies on measures of probabilistic truthlikeness, that are divided into t-measures for statistical probabilities (...) and single case probabilities. The logical notion of probabilistic truthlikeness can be treated as a subcase of deterministic truthlikeness for quantitative theories. In contrast, the epistemic notion of probabilistic truthlikeness creates genuinely new problems, especially for hypotheses about single case probabilities that are evaluated not by comparison to observed frequencies, but by comparison to the truth values of single event statements. By the method of meta-induction, competing theories about single case probabilities can be aggregated into a combined theory with optimal predictive success and epistemic truthlikeness. (shrink)

In this paper I combine the dynamic epistemic logic ofGerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The resultis a new probabilistic dynamic epistemic logic, a logic for reasoning aboutprobability, information, and information change that takes higher orderinformation into account. Probabilistic epistemic models are defined, and away to build them for applications is given. Semantics and a proof systemis presented and a number of examples are discussed, including the MontyHall Dilemma.

We investigate a basic probabilistic dynamic semantics for a fragment containing conditionals, probability operators, modals, and attitude verbs, with the aim of shedding light on the prospects for adding probabilistic structure to models of the conversational common ground.

We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the (...) author. We show that the notions of Zλ- and lexλ-entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, Zλ-entailment is weaker than lexλ-entailment, and both Zλ- and lexλ-entailment are proper generalizations of their classical counterparts. (shrink)

In my article, I present a new version of a probabilistic truth prescribing semantics for natural language indicative conditionals. The proposed truth conditions can be paraphrased as follows: an indicative conditional is true if the corresponding conditional probability is high and the antecedent is positively probabilistically relevant for the consequent or the probability of the antecedent of the conditional equals 0. In the paper, the truth conditions are defended and some of the logical properties of the proposed semantics are (...) described. (shrink)

Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or “associational”) languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is (...) no jump in computational complexity. Along the way we answer several open problems concerning the complexity of well-known probability logics, in particular demonstrating the ${\exists \mathbb {R}}$ -completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability. (shrink)

In the literature, different frameworks of probabilistic epistemic logic have been proposed. Most of these frameworks define knowledge or belief by relational structure. In this paper, we explore the relationship between probability and belief, based on the Lockean thesis, and adopt neighborhood semantics that defines belief directly using probability. We provide a sound and weakly complete axiomatization for our framework. We also try to explain the lottery paradox by modelling it within our framework. Moreover, the paper presents findings concerning (...) the relationship between knowledge, belief and probability within various frameworks. (shrink)

Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilised in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual combinations are compositional, and so can be considered as a function of the semantics of the constituent concepts, or not. While the systematicity and productivity of language provide a strong argument in favor of assuming compositionality, this very assumption is still regularly questioned in both cognitive science and (...) philosophy. Additionally, the principle of semantic compositionality is underspecifi ed, which means that notions of both "strong" and "weak" compositionality appear in the literature. Rather than adjudicating between different grades of compositionality, the framework presented here contributes formal methods for determining a clear dividing line between compositional and non-compositional semantics. In addition, we suggest that the distinction between these is contextually sensitive. Compositionality is equated with a joint probability distribution modeling how the constituent concepts in the combination are interpreted. Marginal selectivity is introduced as a pivotal probabilistic constraint for the application of the Bell/CH and CHSH systems of inequalities. Non-compositionality is equated with a failure of marginal selectivity, or violation of either system of inequalities in the presence of marginal selectivity. This means that the conceptual combination cannot be modeled in a joint probability distribution, the variables of which correspond to how the constituent concepts are being interpreted. The formal analysis methods are demonstrated by applying them to an empirical illustration of twenty-four non-lexicalised conceptual combinations. (shrink)

The goal of standard semantics is to provide truth conditions for the sentences of a given language. Probabilistic Semantics does not share this aim; it might be said instead, if rather cryptically, that Probabilistic Semantics aims to provide belief conditions.The central and guiding idea of Probabilistic Semantics is that each rational individual has ‘within’ him or her a personal subjective probability function. The output of the function when given a certain sentence as input represents the degree of (...) likelihood which the individual would assign to that sentence. One can characterize these functions via a set of axioms, and in the terms of this defined structure develop probabilistic analogues of all important semantical notions. Then, dealing with ‘being given probability 1’ instead of ‘truth,’ one can proceed to give a completely adequate semantics for the particular language under consideration. The axioms delimiting the class of probability functions are, in fact, chosen with this goal and language in mind. (shrink)