Related papers: Taylor expansion in linear logic is invertible
We address the following question: Can we expand an NIP theory by adding a linear order such that the expansion is still NIP? Easily, if acl(A)=A for all A, then this is true. Otherwise, we give counterexamples. More precisely, there is a…
We provide a partial result on Taylor's modularity conjecture, and several related problems. Namely, we show that the interpretability join of two idempotent varieties that are not congruence modular is not congruence modular either, and we…
In this paper, we study the well extension of strict(irreflective) partial well orderings. We first prove that any partially well-ordered structure <A, R> can be extended to a well-ordered one. Then we prove that every linear extension of…
In this paper, we attempt to develop the Schreier theory for two special types extensions of multiplicative Lie algebras.
Proof nets for MLL (unit-free Multiplicative Linear Logic) are concise graphical representations of proofs which are canonical in the sense that they abstract away syntactic redundancy such as the order of non-interacting rules. We argue…
We study the complexity of reachability problems on branching extensions of vector addition systems, which allows us to derive new non-elementary complexity bounds for fragments and variants of propositional linear logic. We show that…
Neural networks (NNs) achieve outstanding performance in many domains; however, their decision processes are often opaque and their inference can be computationally expensive in resource-constrained environments. We recently proposed…
Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…
We define and study multiplicative connections in the tangent bundle of a Lie groupoid. Multiplicative connections are linear connections satisfying an appropriate compatibility with the groupoid structure. Our definition is natural in the…
We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property.…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
Hierarchical graph rewriting is a highly expressive computational formalism that manipulates graphs enhanced with box structures for representing hierarchies. It has provided the foundations of various graph-based modeling tools, but the…
This paper is a continuation of [arXiv:1603.02204]. Exploded layered tropical (ELT) algebra is an extension of tropical algebra with a structure of layers. These layers allow us to use classical algebraic results in order to easily prove…
We show that provability in the implicational fragment of relevance logic is complete for doubly exponential time, using reductions to and from coverability in branching vector addition systems.
We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the…
System I is a proof language for a fragment of propositional logic where isomorphic propositions, such as $A\wedge B$ and $B\wedge A$, or $A\Rightarrow(B\wedge C)$ and $(A\Rightarrow B)\wedge(A\Rightarrow C)$ are made equal. System I enjoys…
We prove that every $L$-bilipschitz mapping $\mathbb{Z}^2\to\mathbb{R}^2$ can be extended to a $C(L)$-bilipschitz mapping $\mathbb{R}^2\to\mathbb{R}^2$ and provide a polynomial upper bound for $C(L)$. Moreover, we extend the result to every…
We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory,…
This paper develops a novel nested sequent proof-search methodology for intuitionistic tense logics (ITLs), supporting finite counter-model extraction. We introduce a new loop-checking method that detects repeating nested sequents using…
We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property…