Related papers: Gradual Classical Logic for Attributed Objects
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
Weighted gradual semantics provide an acceptability degree to each argument representing the strength of the argument, computed based on factors including background evidence for the argument, and taking into account interactions between…
Classical semantics assumes that one can model reference, predication and quantification with respect to a fixed domain of precise referent objects. Non-logical terms and quantification are then interpreted directly in terms of elements and…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
In response to an object presentation, supervised learning schemes generally respond with a parsimonious label. Upon a similar presentation we humans respond again with a label, but are flooded, in addition, by a myriad of associations. A…
We present an elementary introduction to a new logic for reasoning about behaviors that occur over time. This logic is based on temporal type theory. The syntax of the logic is similar to the usual first-order logic; what differs is the…
A gradual semantics takes a weighted argumentation framework as input and outputs a final acceptability degree for each argument, with different semantics performing the computation in different manners. In this work, we consider the…
The recapture relationship is an important element to any understanding of the connexion between different systems of logic. Loosely speaking, one system of logic recaptures another if it is possible to specify a subsystem of the former…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
Much of philosophical logic and all of philosophy of language make empirical claims about the vernacular natural language. They presume semantics under which `and' and `or' are related by the dually paired distributive and absorption laws.…
Linguistic relations in oral conversations present how opinions are constructed and developed in a restricted time. The relations bond ideas, arguments, thoughts, and feelings, re-shape them during a speech, and finally build knowledge out…
Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking…
We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…