Explaining and trusting expert evidence: What is a ‘sufficiently reliable scientific basis’?

Through a series of judicial decisions and Practice Directions, the English courts have developed a rule that expert evidence must have ‘a sufficiently reliable scientific basis to be admitted’. There is a dearth of case-law as to what degree of reliability is ‘sufficient’. This article argues that the test should be interpreted as analogous to one developed in the law of hearsay: expert evidence (scientific or otherwise) must be ‘potentially safely reliable’ in the context of the evidence as a whole. The implications of this test will vary according to the relationship between the expert evidence and the other evidence in the case. The article identifies three main patterns into which this relationship falls. Whether the jury relies upon the evidence will depend upon what they regard as the best explanation of the evidence and how far they trust the expert. Whether their reliance is safe (as a basis for conviction) depends on whether they could rationally rule out explanations consistent with innocence, and whether the degree to which they take the expert’s evidence on trust is consistent with prosecution’s burden of proving the essential elements of its case, including the reliability of any scientific techniques on which it relies

Notions of Anonymous Existence in Martin-L\"of Type Theory

As the groupoid model of Hofmann and Streicher proves, identity proofs in intensional Martin-L\"of type theory cannot generally be shown to be unique. Inspired by a theorem by Hedberg, we give some simple characterizations of types that do have unique identity proofs. A key ingredient in these constructions are weakly constant endofunctions on identity types. We study such endofunctions on arbitrary types and show that they always factor through a propositional type, the truncated or squashed domain. Such a factorization is impossible for weakly constant functions in general (a result by Shulman), but we present several non-trivial cases in which it can be done. Based on these results, we define a new notion of anonymous existence in type theory and compare different forms of existence carefully. In addition, we show possibly surprising consequences of the judgmental computation rule of the truncation, in particular in the context of homotopy type theory. All the results have been formalized and verified in the dependently typed programming language Agda.Comment: 36 pages, to appear in the special issue of TLCA'13 (LMCS

Disquotationalism and the Compositional Principles

What Bar-On and Simmons call 'Conceptual Deflationism' is the thesis that truth is a 'thin' concept in the sense that it is not suited to play any explanatory role in our scientific theorizing. One obvious place it might play such a role is in semantics, so disquotationalists have been widely concerned to argued that 'compositional principles', such as (C) A conjunction is true iff its conjuncts are true are ultimately quite trivial and, more generally, that semantic theorists have misconceived the relation between truth, meaning, and logic. This paper argues, to the contrary, that even such simple compositional principles as (C) have substantial content that cannot be captured by deflationist 'proofs' of them. The key thought is that (C) is supposed, among other things, to affirm the truth-functionality of conjunction and that disquotationalists cannot, ultimately, make sense of truth-functionality. This paper is something of a companion to "The Logical Strength of Compositional Principles"

Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram