Related papers: A continuation semantics of interrogatives that ac…
Up to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic…
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
Higher Type Arithmetic (HA$^w$) is a first-order many-sorted theory. It is a conservative extension of Heyting Arithmetic obtained by extending the syntax of terms to all of System T: the objects of interest here are the functionals of…
Superlatives are used to single out elements with a maximal/minimal property. Semantically, superlatives perform a set comparison: something (or some things) has the min/max property out of a set. As such, superlatives provide an ideal…
Syntax is a latent hierarchical structure which underpins the robust and compositional nature of human language. In this work, we explore the hypothesis that syntactic dependencies can be represented in language model attention…
An S-adic expansion of an infinite word is a way of writing it as the limit of an infinite product of substitutions (i.e., morphisms of a free monoid). Such a description is related to continued fraction expansions of numbers and vectors. A…
Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond ${\bf NP\neq co NP}$. These conjectures formally connect computational complexity with the difficulty of…
Recursive reasoning systems alternate between acquiring new evidence and refining an accumulated understanding. Two design choices are typically left implicit: how to represent the evolving reasoning state, and when to stop iterating. This…
Query answering under existential rules -- implications with existential quantifiers in the head -- is known to be decidable when imposing restrictions on the rule bodies such as frontier-guardedness [BLM10, BLMS11]. Query answering is also…
We introduce the $\omega$-Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture. We believe that if one were to prove the infinitary Vaught's conjecture in a structural way without using techniques from higher recursion…
We explore denotational interpreters: denotational semantics that produce coinductive traces of a corresponding small-step operational semantics. By parameterising our denotational interpreter over the semantic domain and then varying it,…
Existential rules are a very popular ontology-mediated query language for which the chase represents a generic computational approach for query answering. It is straightforward that existential rule queries exhibiting chase termination are…
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…
This Paper investigate sequent calculi for certain weak subintuitionistic logics. We establish that weakening and contraction are height-preserving admissible for each of these calculi, and we provide a syntactic proof for the admissibility…
Deep learning techniques are increasingly popular in the textual entailment task, overcoming the fragility of traditional discrete models with hard alignments and logics. In particular, the recently proposed attention models (Rockt\"aschel…
In this paper, we present an interactive semantics for derivations in an infinitary extension of classical logic. The formulas of our language are possibly infinitary trees labeled by propositional variables and logical connectives. We show…
Lax extensions of set functors play a key role in various areas including topology, concurrent systems, and modal logic, while predicate liftings provide a generic semantics of modal operators. We take a fresh look at the connection between…
Quoted speech is often set off by punctuation marks, in particular quotation marks. Thus, it might seem that the quotation marks would be extremely useful in identifying these structures in texts. Unfortunately, the situation is not quite…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their…