Related papers: Subatomic systems need not be subatomic
This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units…
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
The main goal of the article is testing a new classification algorithm. To this end we apply it to a relevant problem of describing the integrable cases of a subclass of two-dimensional lattices. By imposing the cut-off conditions…
Formal properties represent a cornerstone of the system-correctness proofs based on formal verification techniques such as model checking. Formalizing requirements into temporal properties may be very complex and error prone, due not only…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
Several variants of linear logic have been proposed to characterize complexity classes in the proofs-as-programs correspondence. Light linear logic (LLL) ensures a polynomial bound on reduction time, and characterizes in this way polynomial…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
We establish a set of exact sum rules that relate the interatomic force constants to the frequency-dependent electromagnetic susceptibility of a solid or molecule, thereby generalizing the long-established principles of rototranslational…
The tree automaton completion is an algorithm used for proving safety properties of systems that can be modeled by a term rewriting system. This representation and verification technique works well for proving properties of infinite systems…
In this work we provide algorithmic solutions to five fundamental problems concerning the verification, synthesis and correction of concurrent systems that can be modeled by bounded p/t-nets. We express concurrency via partial orders and…
A theorem of alternatives provides a reduction of validity in a substructural logic to validity in its multiplicative fragment. Notable examples include a theorem of Arnon Avron that reduces the validity of a disjunction of multiplicative…
Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry…
We show that if the structural rules are admissible over a set R of atomic rules, then they are admissible in the sequent calculus obtained by adding the rules in R to G3[mic]. Two applications to pure logic and to the sequent calculus with…
We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is…
We introduce a new data structure for answering connectivity queries in undirected graphs subject to batched vertex failures. Precisely, given any graph G and integer k, we can in fixed-parameter time construct a data structure that can…
Resolution and superposition are common techniques which have seen widespread use with propositional and first-order logic in modern theorem provers. In these cases, resolution proof production is a key feature of such tools; however, the…