Related papers: On Deriving Nested Calculi for Intuitionistic Logi…
Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
This paper shows connections between command injection attacks, continuations, and the Lambek calculus: certain command injections, such as the tautology attack on SQL, are shown to be a form of control effect that can be typed using the…
A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…
We give labeled natural deduction systems for a family of tense logics extending the basic linear tense logic Kl. We prove that our systems are sound and complete with respect to the usual Kripke semantics, and that they possess a number of…
Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…
The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional…
Display calculi are generalized sequent calculi which enjoy a `canonical' cut elimination strategy. That is, their cut elimination is uniformly obtained by verifying the assumptions of a meta-theorem, and is preserved by adding or removing…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
In our previous work, we proposed the logic obtained from full non-associative Lambek calculus by adding a sort of linear-logical modality. We call this logic non-associative non-commutative intuitionistic linear logic ($\mathbf{NACILL}$,…
Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without…
This technical note provides comprehensive derivations of fundamental equations in two-level nested and sequential logit models for analyzing hierarchical choice structures. We present derivations of the Berry (1994) inversion formula,…
Event Extraction bridges the gap between text and event signals. Based on the assumption of trigger-argument dependency, existing approaches have achieved state-of-the-art performance with expert-designed templates or complicated decoding…
A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…
Public announcement logic(PAL) is an extension of epistemic logic (EL) with some reduction axioms. In this paper, we propose a cut-free labelled sequent calculus for PAL, which is an extension of that for EL with sequent rules adapted from…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
The mathematical representation of semantics is a key issue for Natural Language Processing (NLP). A lot of research has been devoted to finding ways of representing the semantics of individual words in vector spaces. Distributional…
Double-negation translations are used to encode and decode classical proofs in intuitionistic logic. We show that, in the cut-free fragment, we can simplify the translations and introduce fewer negations. To achieve this, we consider the…
Detecting semantic arguments of a predicate word has been conventionally modeled as a sentence-level task. The typical reader, however, perfectly interprets predicate-argument relations in a much wider context than just the sentence where…
Simple continued fractions, base-b expansions, Dedekind cuts and Cauchy sequences are common notations for number systems. In this note, first, it is proven that both simple continued fractions and base-b expansions fail to denote real…