Related papers: Classical theorems in the Implicational Propositio…
Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
We isolate a combinatorial property of capacities leading to a construction of proper forcings. Then we show that many classical capacities such as the Newtonian capacity satisfy the property.
Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
In this paper, we study several propositional team logics that are closed under unions, including propositional inclusion logic. We prove that all these logics are expressively complete, and we introduce sound and complete systems of…
Formal transformations somehow resembling the usual derivative are surprisingly common in computer science, with two notable examples being derivatives of regular expressions and derivatives of types. A newcomer to this list is the…
The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness…
In this paper, we present a propositional sequent calculus containing disjoint copies of classical and intuitionistic logics. We prove a cut-elimination theorem and we establish a relation between this system and linear logic.
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
Classical Processes (CP) is a calculus where the proof theory of classical linear logic types communicating processes with mobile channels, a la pi-calculus. Its construction builds on a recent propositions as types correspondence between…
Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…
Here, in a series of articles, we show methods for calculating propositional statements using algebraic polynomials as symbols for the connectives, which are named operators. These polynomials originate from the transformation between the…
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
One way of proving theorems in modal logics is translating them into the predicate calculus and then using conventional resolution-style theorem provers. This approach has been regarded as inappropriate in practice, because the resulting…