Related papers: A Binary Quantifier for Definite Descriptions for …
We discuss the definability of finite graphs in first-order logic with two relation symbols for adjacency and equality of vertices. The logical depth $D(G)$ of a graph $G$ is equal to the minimum quantifier depth of a sentence defining $G$…
Any set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a…
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…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
Free variables occur frequently in mathematics and computer science with ad hoc and altering semantics. We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only…
We consider modal logic extended with the well-known temporal operator 'eventually' and provide a cut-elimination procedure for a cyclic sequent calculus that captures this fragment. The work showcases an adaptation of the reductive…
The paper discusses an applicability criterion for a cutoff regularization in the coordinate representation in the Euclidean space with a dimension larger than two. It is shown that the set of functions satisfying the criterion is not…
This article explores the extension of well-known F1 score used for assessing the performance of binary classifiers. We propose the new metric using probabilistic interpretation of precision, recall, specificity, and negative predictive…
A logic formalism is presented which increases the expressive power of the ID/LP format of GPSG by enlarging the inventory of ordering relations and extending the domain of their application to non-siblings. This allows a concise, modular…
Given a binary form $F \in \mathbb{Z}[X, Y]$, we define its value set to be $\{F(x, y) : (x, y) \in \mathbb{Z}^2\}$. Let $F, G \in \mathbb{Z}[X, Y]$ be two binary forms of degree $d \geq 3$ and with non-zero discriminant. In a series of…
Ill-founded (or non-wellfounded) proof systems have emerged as a natural framework for inductive and coinductive reasoning. In such systems, soundness relies on global correctness criteria, such as the progressivity condition. Ensuring that…
Let $\G$ be a unimodular type I second countable locally compact group and $\wG$ its unitary dual. Motivated by a recent pseudo-differential calculus, we develop a positive Berezin-type quantization with operator-valued symbols defined on…
The adequate use of information measured in a continuous manner along a period of time represents a methodological challenge. In the last decades, most of traditional statistical procedures have been extended for accommodating these…
We say that a first order formula A distinguishes a graph G from another graph G' if A is true on G and false on G'. Provided G and G' are non-isomorphic, let D(G,G') denote the minimal quantifier rank of a such formula. We prove that, if G…
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…
This paper presents a cut-elimination proof for the logic $LG^\omega$, which is an extension of a proof system for encoding generic judgments, the logic $\FOLDNb$ of Miller and Tiu, with an induction principle. The logic $LG^\omega$, just…
We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm, Tstit and Xstit. All calculi presented possess essential structural…
Labeled examples (i.e., positive and negative examples) are an attractive medium for communicating complex concepts. They are useful for deriving concept expressions (such as in concept learning, interactive concept specification, and…
We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear…