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charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Dear all, I have a fully funded 3.5-year PhD position in logic and category theory av= ailable at the Department of Informatics of the University of Sussex, UK. B= elow is a possible project proposal, however I=92m open to discussion and I= =92d be very happy to adapt it to any candidate with a strong interest in l= ogic and category theory, as well as to consider self-proposed projects in = these areas. The position comes with tax-free stipend at a standard rate of =A318,662 pe= r year and fees will be waived (at the UK, EU, or international rate) for 3= .5 years. In addition, the student will have available a one-off Research a= nd Training Support Grant of =A32,000. The student will join the Foundations of Software Systems group at Sussex, = which is fast growing (three new lecturers are joining us this academic yea= r) and comprises researchers in logic, type theory, semantics of programmin= g languages, formal verification, quantum theory, term rewriting, category = theory, and network systems. The university campus is not far from the city= of Brighton, with excellent quality of life (it=92s by the sea) and direct= connections to Gatwick Airport and London. For any information about the position and how to apply, please email me at= a.santamaria@sussex.ac.uk. With kind regards, Alessio Santamaria --- Proposed project title: Categorical semantics of Deep Inference formalisms. Deep Inference is a methodology for designing formal proof systems that gen= eralise Gentzen=92s formalisms of sequent calculus and natural deduction. I= n a Deep Inference formalism one is allowed to apply logical rules to conne= ctives that are arbitrarily deep inside a formula, instead of just the main= connective, hence the name =93deep inference=94. From this simple concept = stem several consequences, here are a few: 1. Proofs can be composed using the same connectives that build up the form= ulae. 2. Structural rules can be reduced, without loss of information, to an atom= ic form. 3. We can extract from a proof a graph, called =93atomic flow=94, which dis= cards the connectives and only keeps track of the atoms, from their creatio= n to their destruction. The compositional nature of deep inference proofs makes category theory a n= atural setting for an algebraic semantics of these proofs. In particular, a= tomic flows are reminiscent of string diagrams for monoidal categories. Ano= ther operation for deep inference proofs that is being currently developed = is substitution of proofs into others, as a generalisation of the usual not= ion of substitution of a formula inside the atom occurrences of another. Fr= om the categorical point of view, in very simple cases, this looks like hor= izontal composition of natural and extranatural transformations. For more d= etails about deep inference, see http://alessio.guglielmi.name/res/cos/ . This project aims to giving a precise, sound and complete categorical seman= tics to deep inference formalisms of various logics with substitution. The = PhD student will need to have a 2:1 degree or equivalent in Computer Scienc= e or Mathematics and a strong interest in logic and/or category theory. You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | = Learn more about Microsoft 365 Groups --_000_LO6P302MB0096F0BB04EB7CE9AB4666ACAD84ALO6P302MB0096GBRP_ Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable

Dear all,

 

I have a fully funded 3.5-year PhD position in lo= gic and category theory available at the Department of Informatics of the U= niversity of Sussex, UK. Below is a possible project proposal, however I=92= m open to discussion and I=92d be very happy to adapt it to any candidate with a strong interest in logic and cat= egory theory, as well as to consider self-proposed projects in these areas.=

 

The position comes with tax-free stipend at a sta= ndard rate of =A318,662 per year and fees will be waived (at the UK, EU, or= international rate) for 3.5 years. In addition, the student will have avai= lable a one-off Research and Training Support Grant of =A32,000.

 

The student will join the Foundations of Software= Systems group at Sussex, which is fast growing (three new lecturers are jo= ining us this academic year) and comprises researchers in logic, type theor= y, semantics of programming languages, formal verification, quantum theory, term rewriting, category theory, and = network systems. The university campus is not far from the city of Brighton= , with excellent quality of life (it=92s by the sea) and direct connections= to Gatwick Airport and London.

For any information about the position and how to= apply, please email me at a.santamaria@sussex.ac.uk.=

 

With kind regards,

Alessio Santamaria

 

---

Proposed project title: Categorical semantics of = Deep Inference formalisms.

 

Deep Inference is a methodology for designing for= mal proof systems that generalise Gentzen=92s formalisms of sequent calculus an= d natural deduction. In a Deep Inference formalism one is allowed to apply logical rule= s to connectives that are arbitrarily deep inside a formula, instead of jus= t the main connective, hence the name =93deep inference=94. From this simpl= e concept stem several consequences, here are a few:

 

1. Proofs can be composed using the same connecti= ves that build up the formulae.

2. Structural rules can be reduced, without loss = of information, to an atomic form.

3. We can extract from a proof a graph, called = =93atomic flow=94, which discards the connectives and only keeps track of t= he atoms, from their creation to their destruction.

 

The compositional nature of deep inference proofs= makes category theory a natural setting for an algebraic semantics of thes= e proofs. In particular, atomic flows are reminiscent of= string diagrams for monoidal categories. Another operation for deep infere= nce proofs that is being currently developed is substitution of proofs into= others, as a generalisation of the usual notion of substitution of a formula inside the atom occurrences of a= nother. From the categorical point of view, in very simple cases, this look= s like horizontal composition of natural and extranatural transformations. For more detail= s about deep inference, see http://alessio.guglielmi.name/res/cos/ .

This project aims to giving a precise, sound and complete categorical semantics to deep inference formalism= s of various logics with substitution. The PhD student will need to have a = 2:1 degree or equivalent in Computer Science or Mathematics and a strong in= terest in logic and/or category theory.

 

 
 
You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message.
 
View group files   |   Leav= e group   |&n= bsp;  Learn more about Microsoft 365 Groups
 
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