Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).
Two formalisms
Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).
Two formalisms
Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).
Two formalisms
Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).
Two formalisms
Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).
Two formalisms
Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).
Two formalisms
Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).
Two formalisms
Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).
Two formalisms
Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).
Two formalisms
Open deduction: composition by (1) connectives and (2) inference rules.
I It exists [22] and it can be taken as a de nition fordeep inference.
I It generalises the sequent calculus byremoving its restrictions.
I Sequents≈`depth-1 inference without full inference composition'.
I Hypersequents≈`depth-2 inference without full inference composition' [2].
I It compresses proofs bycut,dagnessanddepthitself (new, exponentialspeed-up).
I We'll show the main ideas and some results (Lectures 1–5.1).
`Formalism B': open deduction + (3) substitution.
I It almost exists (ongoing work with Bruscoli, Gundersen and Parigot).
I It further compresses proofs bysubstitution(conjectured further superpolynomial speed-up, it is equivalent to Frege + substitution).
I We'll show some ideas and what we think we can get (Lecture 5.2).