Related papers: Proofs as Execution Trees for the {\pi}-Calculus
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple…
We phrase parsing with context-free expressions as a type inhabitation problem where values are parse trees and types are context-free expressions. We first show how containment among context-free and regular expressions can be reduced to a…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
We present a symbolic transition system and bisimulation equivalence for psi-calculi, and show that it is fully abstract with respect to bisimulation congruence in the non-symbolic semantics. A psi-calculus is an extension of the…
Consequence-based reasoning can be used to construct proofs that explain entailments of description logic (DL) ontologies. In the literature, one can find multiple consequence-based calculi for reasoning in the $\mathcal{EL}$ family of DLs,…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…
Cut-introduction is a technique for structuring and compressing formal proofs. In this paper we generalize our cut-introduction method for the introduction of quantified lemmas of the form $\forall x.A$ (for quantifier-free $A$) to a method…
Many abstract interpretation frameworks and analyses for Prolog have been proposed, which seek to extract information useful for program optimization. Although motivated by practical considerations, notably making Prolog competitive with…
We introduce a family of comparative plausibility logics over neighbourhood models, generalising Lewis' comparative plausibility operator over sphere models. We provide axiom systems for the logics, and prove their soundness and…
We present Hypersequent Classical Processes (HCP), a revised interpretation of the "Proofs as Processes" correspondence between linear logic and the {\pi}-calculus initially proposed by Abramsky [1994], and later developed by Bellin and…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
In this paper we show that cut-free derivations in the epsilon format of sequent calculus provide for a non-elementary speed-up w.r.t. cut-free proofs in usual sequent calculi in first-order language.
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
We present a syntactic cut-elimination procedure for the alternation-free fragment of the modal mu-calculus. Cut reduction is carried out within a cyclic proof system, where proofs are finitely branching but may be non-wellfounded. The…
Separation logic is successful for software verification of heap-manipulating programs. Numbers are necessary to be added to separation logic for verification of practical software where numbers are important. However, properties of the…
We introduce derivation depth-a computable metric of the reasoning effort needed to answer a query based on a given set of premises. We model information as a two-layered structure linking abstract knowledge with physical carriers, and…