This chapter is about probabilistic logics: systems of logic in which logical consequence is defined in probabilistic terms. We will classify such systems and state some key references, and we will present one class of probabilistic... more
This chapter is about probabilistic logics: systems of logic in which logical consequence is defined in probabilistic terms. We will classify such systems and state some key references, and we will present one class of probabilistic logics in more detail: those that derive from Ernest Adams' work.
According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the... more
According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that (i) utilises a new class of Bayesian learning methods that are better suited to modelling dynamic and conditional inferences than standard Bayesian conditionalization, (ii) is able to characterise the special value of logically valid argument schemes in uncertain reasoning contexts, (iii) greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and (iv) undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic.
This chapter is about probabilistic logics: systems of logic in which logical consequence is defined in probabilistic terms. We will classify such systems and state some key references, and we will present one class of probabilistic... more
This chapter is about probabilistic logics: systems of logic in which logical consequence is defined in probabilistic terms. We will classify such systems and state some key references, and we will present one class of probabilistic logics in more detail: those that derive from Ernest Adams’ work.
We take coherence based probability logic as the basic reference theory to model human,deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic... more
We take coherence based probability logic as the basic reference theory to model human,deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic and probability in psychology. A study on conditional inferences illustrates our approach. First steps towards a process model of conditional inferences conclude the paper. Key
We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams' Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional... more
We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams' Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided that (ii) φ is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals.
An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the... more
An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if..., then...” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval $[0, 1] $. Not all logically valid ...
Abstract The semantics-pragmatics interface has recently been the focus of an increasing amount of descriptive, theoretical and methodological interest (Turner 1999; Bianchi 2004; Szabó 2005; von Heusinger & Turner... more
Abstract The semantics-pragmatics interface has recently been the focus of an increasing amount of descriptive, theoretical and methodological interest (Turner 1999; Bianchi 2004; Szabó 2005; von Heusinger & Turner 2006). This interest is very welcome, and the ...
We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional... more
We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional $$\varphi \rightarrow \psi$$ φ → ψ to the extent that (i) the conditional probability $$\mathrm{p}(\psi |\varphi )$$ p ( ψ | φ ) is high, provided that (ii) $$\varphi$$ φ is relevant for $$\psi$$ ψ . How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both...
Table of Contents: Explorations in the semantics-pragmatics interface Maj-Britt Mosegaard Hansen & Ken Turner Pages: 7-13 Semantic and pragmatic contributions to information status Betty J. Birner Pages: 14-32 Salience and... more
Table of Contents:
Explorations in the semantics-pragmatics interface
Maj-Britt Mosegaard Hansen & Ken Turner
Pages: 7-13
Semantic and pragmatic contributions to information status
Betty J. Birner
Pages: 14-32
Salience and anaphoric definite noun phrases
Klaus von Heusinger
Pages: 33-53
The unitary procedural semantics of the, this and that
Alex Klinge
Pages: 54-77
Semantic, pragmatic and lexical aspects of the measure phrase + adjective construction
M. Lynne Murphy
Pages: 78-100
Probability logic and conversation
Ken Turner
Pages: 101-136
The semantics of polyphony (and the pragmatics of realization)
Henning Nølke
Pages: 137-160
Grammaticalization and persistence phenomena in two hybrid discourse markers — la preuve and regarde
Corinne Rossari
Pages: 161-179
From pragmatics to semantics: Esto es in formulaic expressions
Salvador Pons Bordería
Pages: 180-206
The role of lexical semantics in semantic change
Jacqueline Visconti
Pages: 207-234
GCI theory and language change
Maj-Britt Mosegaard Hansen and & Richard Waltereit
Pages: 235-268
[This paper is available for download under "Articles" below.]
Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such... more
Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case.
