Anna Laura Suarez

I am a second year PhD student at the University of Birmingham. My supervisor is Achim Jung.


Contact details

Room 218
School of Computer Science
University of Birmingham
Edgbaston
B15 2TT
Birmingham
United Kingdom

My email address is: axs1431[symbol]cs.bham.ac.uk


Research interests

I am interested in pointfree representations of spaces and their connections with logic. In particular I am interested in how pointfree topology (locale theory) can be extended to the bitopological setting.

Background

I completed the Logic Year postgraduate programme at the Institute of Language, Logic and Computation (Amsterdam) in 2017.
I completed my Bachelor's degree in Mathematics at Heriot-Watt University (Edinburgh) in 2016.

Talks and notes

An overview of my current research

I am studying objects called d-frames. We may interpret these in various ways.

(1) They act as pointfree bitopological spaces, in virtue of a Stone-type adjunction between the two categories at play. Bitopological spaces are sets of points equipped with two topologies. They arise naturally when we are dealing with topologies that are described by two coarser topologies. For instance, the opens in the Euclidian topology on the real line have a very complicated order structure. But this topology is generated by upper open intervals and lower ones, and both these structures are much simpler order-theoretically.

(2) They act as representations of four-valued logical theories. The four truth values of these theories are True, False, Neither, and Both. They refine two valued logic in that they take into account not only the truhhood or falsehood of assertions, but also our ability to verify them or refute them. What this means is that in these settings our access to information is imperfect. We may have not enough information (we may be, that is, unable to verify or refute an assertion); or we may have too much information (we may receive false information which both refutes and verifies the same assertion). Hence the two extra truth values. In particular these logical theories give an account of the notion, important in Computer Science, of undecidability.

(3) They act as canonical presentations of certain frames in terms of two generating frames and relations. To obtain a frame from such a presentation in general one takes the free frame generated by the two frames (i.e. their coproduct), and quotients it by the relations. The frames which are presented by d-frames are exactly those such that these relations are in a certain sense finitary . By this we mean that these are relations that only involve elements of the coproduct expressible as finite joins of finite meets of the generators.