David Makinson 
 


Currently Visiting Professor in the Department of Philosophy, Logic and Scientific Method, London School of Economics (LSE). Has been a Senior Research Fellow  in the Department of Computer Science, King’s College London, Chairman of the Department in the American University of Beirut, Lebanon, and Programme Specialist with Unesco.

A short intellectual autobiography, "A tale of five cities", was published in Sven Ove Hansson ed., David Makinson on Classical Methods for Non-Classical Problems. Series: Outstanding Contributions to Logic. Springer, New York, 2014, and is also accessible in the annotated list of publications on this website.

                                         In Beijing 2006

General field of research: logic and its relations with other disciplines, including the logic of belief change, the logic of uncertain reasoning, the logic of norms and normative systems, and a variety of other areas. Early work was on modal logic. More details are given below.

Interim remark 2016-03-24: I have not gotten around to setting up all the links to papers mentioned below, but  for almost all of them such links have been set up in the section "Annotated list of publications".

Most recent

In the last few years, my work has diversified into a number of different topics. These include: an analysis of the role of intelim rules in the generation of intuitionistic logic (ref 69), a general semantic study of intelim rules for classical connectives (ref 73), examination of an inferential valuation system of Tor Sandqvist that yields classical logic (ref 71), an explanation of how one may see relevance logic as defining an extension, rather than a restriction, of classical consequence (ref 72), a review of the scope and limitations of Gödel's Master Argument for his first incompleteness theorem (ref 75), and an as yet unpublished critical comment on the stability theory of belief (ref 76).

Logic of Uncertain Reasoning

In this area, my research has followed three main lines. One was directed to clarifying the logical patterns to be found in qualitative uncertain reasoning, commonly (and rather misleadingly) known as nonmonotonic inference (refs 31, 42). Another, carried out jointly with Peter Gärdenfors, established the basic relationships between nonmonotonic inference and belief revision (refs 35, 40). Most recently (refs 53, 58, 60, 66, B3), I have focussed on the relations between qualitative and probabilistic approaches to uncertain reasoning (ref 63 with Jim Hawthorne), conditional probability in the light of qualitative belief change (ref 68), the concept of a lossy inference rule (ref 70 and ref 74 again with Jim Hawthorne).  

Logic of Belief Change

Perhaps the most frequently cited work is the creation of the so-called AGM account of the logic of belief change, with Carlos Alchourrón and Peter Gärdenfors. This was done in a variety of converging forms: postulational, in terms of partial meet operations, relations of epistemic entrenchment, and safe contraction (refs 20, 23, 24, 25, 26), with also a paper (54) reviewing the ways in which the logics of belief change and uncertain reasoning have led to new ways of doing logic.

Recent papers in the area examine the question of relevance in belief change in the light of the finest splitting theorem (refs 64, 65 with George Kourousias, 67). 

Logic of Uncertain Reasoning

In this area, my research has followed three main lines.

One was directed to clarifying the logical patterns to be found in qualitative uncertain reasoning, commonly (and rather misleadingly) known as nonmonotonic inference (refs 31, 42).

Another, carried out jointly with Peter Gärdenfors, established the basic relationships between nonmonotonic inference and belief revision (refs 35, 40).

More recently (refs 53, 58, 60, 66, B3), I have focussed on the relations between qualitative and probabilistic approaches to uncertain reasoning (ref 63 with Jim Hawthorne), conditional probability in the light of qualitative belief change (ref 68), the concept of a lossy inference rule (ref 70 and ref 74 again with Jim Hawthorne).  

Logic of Norms and Normative Systems

In the logic of norms (also known as deontic logic), earlier publications (refs 27 and 30) analyse the Hohfeld classification of rights relationships and its application to real-life rights claims (particularly collective rights)

More recent work reconstructs the logic of norms in accord with the philosophical position that norms lack truth values (ref 50), developing into a general theory of input/output logics as a framework for conditional directives and permissions (refs 51, 52, 54, 56).

Other Areas of Logic

Some of my work does not fall squarely into any of the above categories. One paper (ref 43) separates combinatorial from decision-theoretic components in Arrow's impossibility theorem and the closely related Blair/Bordes/Kelly/Suzumura theorem in the theory of collective preference, providing a particularly elegant proof of those results. Another (ref 61) articulates the fascinating concept of logical friendliness, studying its implicit manifestations in the literature of the last hundred and fifty years, as well as its properties. A third formulates the concept of parallel interpolation and continues Parikh's analysis of splitting in classical propositional logic (refs 64, 65, with George Kourousias, also 67).

Early Work in Modal Logic

Early work focussed largely on modal logic. Perhaps the most cited contribution in this area was the adaptation, in my1965 D.Phil. thesis and a following publication (ref 6), of the maximal consistent set method, then well-known in classical propositional and predicate logic (Lindenbaum, Henkin), to serve as a tool for establishing completeness results in modal and other non-classical logics, where it is now a standard procedure.

Also often mentioned is the discovery (ref 8) of the first simple and natural propositional logic lacking the finite model property; and formulation (ref 10) of a generalised notion of relational model for modal logic, bringing the relational account into harmony with the algebraic one.

Another, quite ignored at the time of its publication in 1971 but often cited in recent years (ref 12), proves the first (and still the main) embedding theorems for modal logics.


Recent Books

The graduate textbook Bridges from Classical to Nonmonotonic Logic published in 2005 and is available from Amazon.co.uk.

Table of contents and preface on view here

Polish translation, published in 2008.

 

A revised 2nd edition of Sets, Logic and Maths for Computing appeared in 2012.
 

A Chinese translation of the first edition was published by Tsinghua University Press in May 2010.

Reviews of first edition
ACM Computing Reviews January 2009 and Amazon Books (USA) customer review Sept 2009.

David Makinson on Classical Methods for Non-Classical Problems (ed. Sven Ove Hansson in the series Outstanding Contributions to Logic)  appeared in 2014.

Files

Annotated List of publications with downloadable copies of most of them

full cv (pdf)
 
Contact info

Email

david(dot)makinson
(at)gmail(dot)com

or

d(dot)makinson
(at)lse(dot)ac(dot)uk

Postal address

Philosophy Department, LSE, Houghton St, London WC2A 2AE, UK