Francesco A. Genco

Gödel logic: From natural deduction to parallel computation

Propositional Gödel logic G extends intuitionistic logic with the non-constructive principle of linearity (A → B) ∨ (B → A). We introduce a Curry-Howard correspondence for G and show that a simple natural deduction calculus can be used as a typing system. The resulting functional language extends the simply typed λ-calculus via a synchronous communication mechanism between parallel processes, which increases its expressive power. The normalization proof employs original termination arguments and proof transformations implementing forms of code mobility. Our results provide a computational interpretation of G, thus proving A. Avrons 1991 thesis.

Hypersequents and Systems of Rules: Embeddings and Applications

We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of the benefits of locality for 2-systems, analyticity results for a large class of such systems, and a rewriting of hypersequent rules as natural deduction rules.

Substructural logics: semantics, proof theory, and applications. report on the second SYSMICS workshop.

Substructural logics: semantics, proof theory, and applications is the second workshop within the project SYSMICS (Syntax meets Semantics - Methods, Interactions, and Connections in Substructural logics). It was held in Vienna at the Faculty of Mathematics, University of Vienna, from 26 -- 28 February 2018.

M\=im\=a\d{m}s\=a deontic logic: proof theory and applications

Starting with the deontic principles in Măi¾źmăi¾źai¾źi¾źsăi¾ź texts we introduce a new deontic logic. We use general proof-theoretic methods to obtain a cut-free sequent calculus for this logic, resulting in decidability, complexity results and neighbourhood semantics. The latter is used to analyse a well known example of conflicting obligations from the Vedas.

Măźmăźáźźsăź Deontic Logic: Proof Theory and Applications

Starting with the deontic principles in Măi¾źmăi¾źai¾źi¾źsăi¾ź texts we introduce a new deontic logic. We use general proof-theoretic methods to obtain a cut-free sequent calculus for this logic, resulting in decidability, complexity results and neighbourhood semantics. The latter is used to analyse a well known example of conflicting obligations from the Vedas.

Mīmāṃsā Deontic Logic: Proof Theory and Applications

Starting with the deontic principles in Măi¾źmăi¾źai¾źi¾źsăi¾ź texts we introduce a new deontic logic. We use general proof-theoretic methods to obtain a cut-free sequent calculus for this logic, resulting in decidability, complexity results and neighbourhood semantics. The latter is used to analyse a well known example of conflicting obligations from the Vedas.