Related papers: Proof-theoretic Semantics for the Logic of Bunched…
The fruits of science are relationships made comprehensible, often by way of approximation. While deep learning is an extremely powerful way to find relationships in data, its use in science has been hindered by the difficulty of…
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…
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…
An involutive Stone algebra (IS-algebra) is a structure that is simultaneously a De Morgan algebra and a Stone algebra (i.e. a pseudo-complemented distributive lattice satisfying the well-known Stone identity ~xv~~x=1). IS-algebras have…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
Two prominent challenges in explainability research involve 1) the nuanced evaluation of explanations and 2) the modeling of missing information through baseline representations. The existing literature introduces diverse evaluation…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
Logical fallacy uses invalid or faulty reasoning in the construction of a statement. Despite the prevalence and harmfulness of logical fallacies, detecting and classifying logical fallacies still remains a challenging task. We observe that…
Based on a variation of the BIP operational semantics using the offer predicate introduced in our previous work, we extend the algebras used to model glue operators in BIP to encompass priorities. This extension uses the Algebra of Causal…
We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms,…
We define base-extension semantics (Bes) using atomic systems based on sequent calculus rather than natural deduction. While traditional Bes aligns naturally with intuitionistic logic due to its constructive foundations, we show that…
Pomset logic and BV are both logics that extend multiplicative linear logic (with Mix) with a third connective that is self-dual and non-commutative. Whereas pomset logic originates from the study of coherence spaces and proof nets, BV…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
Bilateralism is the position according to which assertion and rejection are conceptually independent speech acts. Logical bilateralism demands that systems of logic provide conditions for assertion and rejection that are not reducible to…
While there exist several reasoners for Description Logics, very few of them can cope with uncertainty. BUNDLE is an inference framework that can exploit several OWL (non-probabilistic) reasoners to perform inference over Probabilistic…
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex…
One of the most pressing issues in AI in recent years has been the need to address the lack of explainability of many of its models. We focus on explanations for discrete Bayesian network classifiers (BCs), targeting greater transparency of…
We consider logic-based argumentation in which an argument is a pair (Fi,al), where the support Fi is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by De) that entails the claim al (a formula). We…
Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They…
We propose a hybrid architecture that integrates decision tree-based symbolic reasoning with the generative capabilities of large language models (LLMs) within a coordinated multi-agent framework. Unlike prior approaches that loosely couple…