Related papers: Considerations on Everett J. Nelson's connexive lo…
We introduce and investigate a family of consequence relations with the goal of capturing certain important patterns of data-driven inference. The inspiring idea for our framework is the fact that data may reject, possibly to some degree,…
The inverse problem of statistical mechanics involves finding the minimal Hamiltonian that is consistent with some observed set of correlation functions. This problem has received renewed interest in the analysis of biological networks; in…
Linear logic has provided new perspectives on proof-theory, denotational semantics and the study of programming languages. One of its main successes are proof-nets, canonical representations of proofs that lie at the intersection between…
This paper extends the literature on the strict-tolerant logical approach by applying its methods to intuitionistic and minimal logic. In short, the strict-tolerant approach modifies the usual notion of logical consequence by stipulating…
We consider a family of two-valued "fully evaluated left-sequential logics" (FELs), of which Free FEL (defined by Staudt in 2012) is most distinguishing (weakest) and immune to atomic side effects. Next is Memorising FEL, in which…
This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational…
Language models' (LMs) proficiency in handling deterministic symbolic reasoning and rule-based tasks remains limited due to their dependency implicit learning on textual data. To endow LMs with genuine rule comprehension abilities, we…
This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from COH to FIN commuting with the additive and multiplicative structure of linear logic. What makes this correspondence…
In this paper, we use a new method to prove cut-elimination of weak intuitionistic tense logic. This method focuses on splitting the contraction rule and cut rules. Further general theories and applications of this method shall be developed…
The application of rough set theory in incomplete information systems is a key problem in practice since missing values almost always occur in knowledge acquisition due to the error of data measuring, the limitation of data collection, or…
Relation extraction is the task of determining the relation between two entities in a sentence. Distantly-supervised models are popular for this task. However, sentences can be long and two entities can be located far from each other in a…
We generalise the Blok-J\'onsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and J\'onsson admit, in place…
The recapture relationship is an important element to any understanding of the connexion between different systems of logic. Loosely speaking, one system of logic recaptures another if it is possible to specify a subsystem of the former…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
Conventional approaches to relation extraction usually require a fixed set of pre-defined relations. Such requirement is hard to meet in many real applications, especially when new data and relations are emerging incessantly and it is…
Sentence embeddings encode natural language sentences as low-dimensional dense vectors. A great deal of effort has been put into using sentence embeddings to improve several important natural language processing tasks. Relation extraction…
This is an expanded lecture note for "Masterclass on sofic groups and applications to operator algebras" (University of Copenhagen, 5-9 November 2012). It is about algebraic aspects of the Connes Embedding Conjecture. It contains new proofs…
I argue that John Norton's notions of empirical, hypothetical, and counterfactual possibility can be successfully used to analyze counterintuitive examples of physical possibility and align better with modal intuitions of practicing…
Our manuscript studies linear temporal (with UNTIL and NEXT) logic based at a conception of intransitive time. non-transitive time. In particular, we demonstrate how the notion of knowledge might be represented in such a framework (here we…
The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…