There is renewed interest in the logic of discovery as well as in the position that there is no reason for philosophers to bother with it. This essay shows that the traditional, philosophical arguments for the latter position are bankrupt. Moreover, no interesting defense of the philosophical irrelevance or impossibility of the logic of discovery can be formulated or defended in isolation from computation-theoretic considerations.

We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in (...) contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented. (shrink)

From the initial analysis of John Morris in 1976 about if computers can lie, I have presented my own treatment of the problem using what can be called a computational lying procedure. One that uses two Turing Machines. From there, I have argued that such a procedure cannot be implemented in a Turing Machine alone. A fundamental difficulty arises, concerning the computational representation of the self-knowledge a machine should have about the fact that it is lying. Contrary to Morris’ claim, (...) I have thus suggested that computers – as far as they are Turing Machines – cannot lie. Consequently, I have claimed that moral agency attribution to a robot or any other automated AI system, cannot be made, strictly grounded on imitating behaviors. Self-awareness as an ontological grounding for moral attribution must be evoked. This can pose a recognition problem from our part, should the sentient system be the only agent capable of acknowledging its own sentience. (shrink)

From the initial analysis of John Morris in 1976 about if computers can lie, I have presented my own treatment of the problem using what can be called a computational lying procedure. One that uses two Turing Machines. From there, I have argued that such a procedure cannot be implemented in a Turing Machine alone. A fundamental difficulty arises, concerning the computational representation of the self-knowledge a machine should have about the fact that it is lying. Contrary to Morris’ claim, (...) I have thus suggested that computers – as far as they are Turing Machines – cannot lie. Consequently, I have claimed that moral agency attribution to a robot or any other automated AI system, cannot be made, strictly grounded on imitating behaviors. Self-awareness as an ontological grounding for moral attribution must be evoked. This can pose a recognition problem from our part, should the sentient system be the only agent capable of acknowledging its own sentience. (shrink)

Abstract The notion of necessary new terms (predicates) is proposed. It is shown that necessary new predicates in first?order logic must be directly, recursively defined. I present a first?order inductive learning algorithm that introduces new necessary predicates to model scientific revolution in which a new language is adopted. I demonstrate that my learning system can learn a genetic theory with theoretical terms which, after being induced by my system, can be interpreted as either types of genetic properties (dominant or recessive) (...) or genes, depending on the representation of the hypotheses of the same theoretical terms. (shrink)

Alternative models of idealized scientific inquiry are investigated and compared. Particular attention is devoted to paradigms in which a scientist is required to determine the truth of a given sentence in the structure giving rise to his data.

A paradigm of scientific discovery is defined within a first-order logical framework. It is shown that within this paradigm there exists a formal scientist that is Turing computable and universal in the sense that it solves every problem that any scientist can solve. It is also shown that universal scientists exist for no regular logics that extend first-order logic and satisfy the Löwenheim-Skolem condition.

The paper investigates learning functions for first order languages. Several types of convergence and identification in the limit are defined. Positive and negative results on learning problems are presented throughout the paper.