Related papers: Natural Deduction for Assertibility and Deniabilit…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
We investigate the possibility of distinguishing among different causal relations starting from a limited set of marginals. Our main tool is the notion of adhesivity, that is, the extension of probability or entropies defined only on…
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
We extend the $ASPIC^+$ framework for structured argumentation so as to allow applications of the reasoning by cases inference scheme for defeasible arguments. Given an argument with conclusion `$A$ or $B$', an argument based on $A$ with…
The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
When agents devise plans for execution in the real world, they face two important forms of uncertainty: they can never have complete knowledge about the state of the world, and they do not have complete control, as the effects of their…
We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form "If $\sim A$, then $A$", should not hold,…
This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
This paper presents a method to explain the knowledge encoded in a convolutional neural network (CNN) quantitatively and semantically. The analysis of the specific rationale of each prediction made by the CNN presents a key issue of…
Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed sometimes, in both everyday discourse and academic research. This indicates that it is necessary to…
We give a new proof of the decidability of reachability in alternating pushdown systems, showing that it is a simple consequence of a cut-elimination theorem for some natural-deduction style inference systems. Then, we show how this result…
In this paper we show that two seemingly unrelated problems in economics, the hypothesis of integrability and the hypothesis of additive separability are linked by the absence of curvature of connections on webs naturally associated with…
Existing tools for explaining complex models and systems are associational rather than causal and do not provide mechanistic understanding. We propose a new notion called counterfactual explainability for causal attribution that is…
We formulate argumentative relation classification (support vs. attack) as a text-plausibility ranking task. To this aim, we propose a simple reconstruction trick which enables us to build minimal pairs of plausible and implausible texts by…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it. Assuming such a structure we show that the semantics of various natural language…
While most approaches to automatically recognizing entailment relations have used classifiers employing hand engineered features derived from complex natural language processing pipelines, in practice their performance has been only…