Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater (2014)

Abstract

This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic programming (LP) to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.

Keywords:

• Nonmonotonic logic
• logic programming
• system 1
• probability
• reasoning to interpretation

Acknowledgment

The authors would like to thank Laura Martignon for her helpful comments on this paper. Keith Stenning wishes to acknowledge support from the German DFG under SPP 1516.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ We use inferential strength here as a term neutral between kinds of uncertainty.

² Over (2009)

³ We disregard negations for the moment.

⁴ Cummins uses ‘‘disablers’’ where we retain ‘‘abnormalities’’ in the technical sense from logic programming, simply for exceptions.

⁵ Of a strand of research to use a fragment of classical logic as a computer programming language which eventuated in PROLOG (the history is described in Kowalski, 1988).

⁶ AC inferences are valid in LP, unlike classical logic, precisely when no alternative causes are in the closed-world model.

⁷ At least the local collection of conditional frequencies by ‘monitoring neurons’ in the neural net implementation of LP.