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Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated…

Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…

Many researchers want to unify probability and logic by defining logical probability or probabilistic logic reasonably. This paper tries to unify statistics and logic so that we can use both statistical probability and logical probability…

Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced…

It is well know that basic conditionals satisfy some desirable basic logical and probabilistic properties, such as the compound probability theorem, but checking the validity of these becomes trickier when we switch to compound and iterated…

Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential…

In this work we describe preferential Description Logics of typicality, a nonmonotonic extension of standard Description Logics by means of a typicality operator T allowing to extend a knowledge base with inclusions of the form T(C) v D,…

There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case where the system is argumentation…

We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly…

Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…

The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…

Statistical Relational Models and, more recently, Probabilistic Programming, have been making strides towards an integration of logic and probabilistic reasoning. A natural expectation for this project is that a probabilistic logic…

Aristotle's discussions on modal syllogistic have often been viewed as error-prone and have garnered significant attention in the literature due to historical and philosophical interests. However, from a contemporary standpoint, they also…

Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…

We present a computable algorithm that assigns probabilities to every logical statement in a given formal language, and refines those probabilities over time. For instance, if the language is Peano arithmetic, it assigns probabilities to…

The paper demonstrates that strict adherence to probability theory does not preclude the use of concurrent, self-activated constraint-propagation mechanisms for managing uncertainty. Maintaining local records of sources-of-belief allows…

This paper is an attempt to bring together two approaches to language analysis. The possible use of probabilistic information in principle-based grammars and parsers is considered, including discussion on some theoretical and computational…

Functional Distributional Semantics provides a computationally tractable framework for learning truth-conditional semantics from a corpus. Previous work in this framework has provided a probabilistic version of first-order logic, recasting…

I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an…