Kripke Semantics for Intuitionistic Łukasiewicz Logic

Add to your list(s) Download to your calendar using vCal

• Paulo Oliva (Queen Mary, University of London)
• Friday 13 May 2022, 14:00-15:00
• LG23, SoCS and Zoom (see abstract for link).

If you have a question about this talk, please contact Tom de Jong.

Zoom details

• Link: https://bham-ac-uk.zoom.us/j/81873335084?pwd=T1NaUFg2U1l6d0RLL2RlTzFBam1IUT09
• Meeting ID: 818 7333 5084
• Passcode: 217

Abstract

In this talk I’ll present a generalization of the Kripke semantics of intuitionistic logic IL appropriate for intuitionistic Łukasiewicz logic IŁL – a logic in the intersection between IL and (classical) Łukasiewicz logic. This generalised Kripke semantics is based on the poset sum construction, used in Bova and Montagna (Theoret Comput Sci 410(12):1143–1158, 2009) to show the decidability (and PSPACE -completeness) of the quasiequational theory of commutative, integral and bounded GBL -algebras. The main idea is that w⊩ψ – which for IŁL is a relation between worlds w and formulas ψ, and can be seen as a function taking values in the Booleans, i.e. (w⊩ψ)∈𝔹 – becomes a function taking values in the unit interval, i.e. (w⊩ψ)∈[0,1]. An appropriate monotonicity restriction needs to be put on such functions (which we then call sloping functions) in order to ensure soundness and completeness of the semantics. Based on paper [1], joint work with Andrew Lewis-Smith and Edmund Robinson.

References

[1] A. Lewis-Smith, P. Oliva, E. Robinson, Kripke Semantics for Intuitionistic Łukasiewicz Logic. Studia Logica, 109:313–339, 2021.

This talk will be chaired by Martin Escardo.

This talk is part of the Theoretical computer science seminar series.

This talk is included in these lists:

• Computer Science Departmental Series
• Computer Science Distinguished Seminars
• LG23, SoCS and Zoom (see abstract for link)
• Theoretical computer science seminar
• computer sience

Note that ex-directory lists are not shown.