11 citations · 72 across the 39 of their papers we have counts for
16 papers · 1 filter
Gödel's Natural Deduction
Kosta Dosen, Milos Adzic
This is a companion to a paper by the authors entitled "Gödel on deduction", which examined the links between some philosophical views ascribed to Gödel and general proof theory. W…
Gödel on Deduction
Kosta Dosen, Milos Adzic
This is an examination, a commentary, of links between some philosophical views ascribed to Gödel and general proof theory. In these views deduction is of central concern not only…
Gödel's Notre Dame Course
Milos Adzic, Kosta Dosen
This is a companion to a paper by the authors entitled "Gödel's natural deduction", which presented and made comments about the natural deduction system in Gödel's unpublished note…
Representing Conjunctive Deductions by Disjunctive Deductions
Kosta Dosen, Zoran Petric
A skeleton of the category with finite coproducts D freely generated by a single object has a subcategory isomorphic to a skeleton of the category with finite products C freely gen…
On Sets of Premises
Kosta Dosen
Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we in…
Shuffles and Concatenations in Constructing of Graphs
K. Dosen, Z. Petric
This is an investigation of the role of shuffling and concatenating in the theory of graph drawing. A simple syntactic description of these and related operations is proved complet…
Isomorphic Formulae in Classical Propositional Logic
K. Dosen, Z. Petric
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classic…
Coherence for Modalities
K. Dosen, Z. Petric
Positive modalities in systems in the vicinity of S4 and S5 are investigated in terms of categorial proof theory. Coherence and maximality results are demonstrated, and connections…
Coherence in Linear Predicate Logic
K. Dosen, Z. Petric
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-orde…
Equality of Proofs for Linear Equality
K. Dosen, Z. Petric
This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties…
Negation and Involutive Adjunction
K. Dosen, Z. Petric
This note analyzes in terms of categorial proof theory some standard assumptions about negation in the absence of any other connective. It is shown that the assumptions for an invo…
A Note on the Set-Theoretic Representation of Arbitrary Lattices
K. Dosen
Every lattice is isomorphic to a lattice whose elements are sets of sets, and whose operations are intersection and an operation extending the union of two sets of sets A and B by…
A Brauerian Representation of Split Preorders
K. Dosen, Z. Petric
Split preorders are preordering relations on a domain whose composition is defined in a particular way by splitting the domain into two disjoint subsets. These relations and the as…
Generality of Proofs and its Brauerian Representation
K. Dosen, Z. Petric
The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are i…
Identity of Proofs Based on Normalization and Generality
K. Dosen
In general proof theory there are two approaches to the question of identity criteria for proofs. The first approach, which stems from Prawitz, Kreisel and Lambek, and is based on…
On Permuting Cut with Contraction
Mirjana Borisavljevic, Kosta Dosen, Zoran Petric
The paper presents a cut-elimination procedure for intuitionistic propositional logic in which cut is eliminated directly, without introducing the multiple-cut rule mix, and in whi…