Related papers: Non-contractive logics, Paradoxes, and Multiplicat…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…
We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
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…
Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
First-order logic, and quantifiers in particular, are widely used in deductive verification. Quantifiers are essential for describing systems with unbounded domains, but prove difficult for automated solvers. Significant effort has been…
Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment to contexts involving relations of arity greater than two. Quantifiers in this logic are used in…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
A logical system derived from linear logic and called QMLL is introduced and shown able to capture all unitary quantum circuits. Conversely, any proof is shown to compute, through a concrete GoI interpretation, some quantum circuits. The…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
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…