Related papers: A semantic account of strong normalization in Line…
When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is complete for the class of sets which are the…
The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic…
This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier $I$. $I$ forms a formula from two…
Succinctness is a natural measure for comparing the strength of different logics. Intuitively, a logic L_1 is more succinct than another logic L_2 if all properties that can be expressed in L_2 can be expressed in L_1 by formulas of…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear behaviour. Concretely, we define…
We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational logic networks with linear size…
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…
We examine when differentially flat nonlinear control systems with more than two inputs can be rendered static feedback linearizable by a minimal number of prolongations of suitably chosen inputs after applying a static input…
Can a neural network minimizing cross-entropy learn linearly separable data? Despite progress in the theory of deep learning, this question remains unsolved. Here we prove that SGD globally optimizes this learning problem for a two-layer…
Most deep neural networks are considered to be black boxes, meaning their output is hard to interpret. In contrast, logical expressions are considered to be more comprehensible since they use symbols that are semantically close to natural…
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…
We show how definite extended logic programs can be used for defining and reasoning with rough sets. Moreover, a rough-set-specific query language is presented and an answering algorithm is outlined. Thus, we not only show a possible…
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…
Large language models have evolved to process multiple modalities beyond text, such as images and audio, which motivates us to explore how to effectively leverage them for graph reasoning tasks. The key question, therefore, is how to…
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…