Jaskowski and the Jains

In 1948 Jaśkowski introduced the first discursive logic. The main technical idea was to take what holds to be what is true at some possible world. Some 2,000 years earlier, Jain philosophers had advocated a similar idea, in their doctrine of syādvāda. Of course, these philosophers had no knowledge of contemporary logical notions; but the techniques pioneered by Jaśkowski can be deployed to make the Jain ideas mathematically precise. Moreover, Jain ideas suggest a new family of logics: many-valued discursive logics. In this talk, I will explain all these matters.

The automata-logic connection

This talk is a selective history of ideas on the tight relation between recognisability by computing devices and definability by logical formulas. I will focus on one such class of results that relates finite-state automata and monadic second-order logic. I will provide a survey of the basic concepts, results, and proofs. By way of applications of this theory, I will mention how it supplies optimal solutions to (Church's) synthesis problem, i.e., the problem of computing a program realising a given logical specification, which is finding application in artificial intelligence.

This talk aims to be self-contained for an audience with a background in elementary concepts in logic and computation, as found in typical undergraduate courses.

A Counterfactual History of Modal Logic

What do you think of when you think of the discovery of modal logic? Is it Aristotle’s syllogistic involving necessity, possibility, and contingency? Is it CI Lewis’s criticism of PM? Is it Oskar Becker’s different modal systems? Maybe Ruth Barcan Marcus’s modal predicate logic leaps to mind? Or maybe you’re the sort who grumbles along with WV Quine against the whole bad business? We can accept all of those as normal answers. But it’s a pretty safe bet that among the normal answers few would include 20th century feminist thought. This is a talk about what could have been.

The history of modal logic provides a case study of how logic and ideology connect, and the talk will illustrate this with respect to some recent feminist thought about modal logic.

Proof-theoretic approaches to Epistemic Modal Logic

Epistemology, the study of knowledge, has a long and rich tradition in philosophy. Questions about what we know can be traced to early Greek philosophers. On the other hand, the formal study of the notion of knowledge is more recent. Thanks to developments in modal logic, propositional attitudes like “a knows φ” received a formal logical analysis, making use of the relational possible-worlds semantics. Epistemic modal logic is the result of this study, the branch of modal logic that deals with knowledge. This results in the usual focus in formal studies of knowledge being in terms of semantics. In this talk, I will defend a proof-theoretical approach to Epistemic Modal Logic. In particular, I will present a labelled goal-oriented proof-system.

Logic without Metaphysics

The theme of this talk is that in logic, metaphysical ideas can be useful as metaphors and initial stimulants, but they should be kept at an arm’s length, never taken literally. It is illustrated by four examples, taken from Boole (indefinite symbols), Frege (senses), possible worlds semantics (startreks and dialetheism) and proof-theoretic semantics (intelim harmony). Disagreement is expected.