Upcoming Events

Logic Colloquium

October 22, 2021, 4:10 PM

https://berkeley.zoom.us/j/94041701380?pwd=dVBobHNqSGNjT2ttdVpEMWxmcG93dz09
Registration with Zoom is required for access.

Adam Bjorndahl
Associate Professor of Philosophy, Carnegie Mellon University

The Epistemology of Nondeterminism

Propositional dynamic logic (PDL) is a framework for reasoning about nondeterministic program executions (or, more generally, nondeterministic actions). In this setting, nondeterminism is taken as a primitive: a program is nondeterministic iff it has multiple possible outcomes. But what does “possible” mean, here? This talk explores an epistemic interpretation: working in an enriched logical setting, we represent nondeterminism as a relationship between a program and an agent deriving from the agent’s (in)ability to adequately measure the dynamics of the program execution. More precisely, using topology and the framework of dynamic topological logic, we show that dynamic topological models can be used to interpret the language of PDL in a manner that captures the intuition above, and moreover that continuous functions in this setting correspond exactly to deterministic processes. We prove that certain axiomatizations of PDL remain sound and complete with respect to corresponding classes of dynamic topological models. We also extend the framework to incorporate knowledge using the machinery of subset space logic, and show that the topological interpretation of public announcements coincides exactly with a natural interpretation of test programs. Finally, we sketch a generalization of the topological paradigm in which the distinction between action and measurement (i.e, between functions and opens) is erased, highlighting some preliminary results in this direction.

Logic Colloquium

November 05, 2021, 4:10 PM

https://berkeley.zoom.us/j/94041701380?pwd=dVBobHNqSGNjT2ttdVpEMWxmcG93dz09
Registration with Zoom is required for access.

Snow Zhang
Bersoff Faculty Fellow in Philosophy, New York University

Countable additivity, conglomerability and the continuum hypothesis

TBA

Logic Colloquium

November 19, 2021, 4:10 PM

https://berkeley.zoom.us/j/94041701380?pwd=dVBobHNqSGNjT2ttdVpEMWxmcG93dz09
Registration with Zoom is required for access.

Joel (Ronnie) Nagloo
Associate Professor of Mathematics, University of Illinois Chicago

TBA

TBA

Logic Colloquium

December 03, 2021, 4:10 PM

https://berkeley.zoom.us/j/94041701380?pwd=dVBobHNqSGNjT2ttdVpEMWxmcG93dz09
Registration with Zoom is required for access.

Thomas Icard
Associate Professor of Philosophy, Stanford University

Interleaving Logic and Counting

Reasoning with quantifiers in natural language combines logical and arithmetical features, transcending divides between qualitative and quantitative. This practice blends with inference patterns in “grassroots mathematics” such as pigeon-hole principles. Our topic is this cooperation of logic and counting, studied with small systems and gradually moving upward. We start with monadic first-order logic with counting. We provide normal forms that allow for axiomatization, determine which arithmetical notions are definable, and conversely, discuss which logical notions can be defined out of arithmetical ones, and what sort of (non-)classical logics are induced. Next we study a series of strengthenings in the same style, including second-order versions, systems with multiple counting, and a new modal logic with counting. As a complement to our fragment approach, we also discuss another way of controlling complexity: changing the semantics of counting to reason about “mass” or other aggregating notions than cardinalities. Finally, we return to natural language, confronting the architecture of our formal systems with linguistic quantifier vocabulary, modules such as monotonicity reasoning, and procedural semantics via semantic automata. We conclude with some thoughts on further entanglements of logic and counting in formal systems, on rethinking the qualitative/quantitative divide, and on empirical aspects of our findings. Joint work with Johan van Benthem.