Related papers: Grading Adjoint Logic
Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a…
The implication relationship between subsystems in Reverse Mathematics has an underlying logic, which can be used to deduce certain new Reverse Mathematics results from existing ones in a routine way. We use techniques of modal logic to…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…
Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the…
In this chapter, we introduce a new dialogical system for first order classical logic which is close to natural language argumentation, and we prove its completeness with respect to usual classical validity. We combine our dialogical system…
Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that…
This paper introduces a logical system, called BV, which extends multiplicative linear logic by a non-commutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far it is not achieved…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
Deductive verification techniques based on program logics (i.e., the family of Floyd-Hoare logics) are a powerful approach for program reasoning. Recently, there has been a trend of increasing the expressive power of such logics by…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the…