In this thesis, I present an associative diagram algebra that is a faithful representation of a particular Temperley–Lieb algebra of type affine C, which has a basis indexed by the fully commutative elements of the Coxeter group of the same type. The Coxeter group of type affine C contains an infinite number of fully commutative elements, and so the corresponding Temperley–Lieb algebra is of in...

The Markov condition describes the conditional independence relations present in a causal model that are consequent to its graphical structure, whereas the faithfulness assumption presumes that there are no other independencies in the model. Cartwright argues that causal inference methods have limited applicability because the Markov condition cannot always be applied to domains, and gives an e...

0. Introduction In several Latin American dialects, Spanish obstruent consonants participate in a process of partial voicing assimilation when they appear in syllable final position. (1) /raskar/ à [rÜ as.kar] 'to scratch' /rasgar/ à [rÜ as z .Far] 1 'to rip' /admirar/ à [aD.mi.rar] 'to admire' /adxuntar/ à [aD T .xun5 .tar] 'to adjoin' In this paper, I develop a novel analysis of this process ...

Maier et al. (2010) introduced the relational causal model (RCM) for representing and inferring causal relationships in relational data. A lifted representation, called abstract ground graph (AGG), plays a central role in reasoning with and learning of RCM. The correctness of the algorithm proposed by Maier et al. (2013a) for learning RCM from data relies on the soundness and completeness of AG...

Evaluating an explanation's faithfulness is desired for many reasons such as trust, interpretability and diagnosing the sources of model's errors. In this work, which focuses on NLI task, we introduce methodology Faithfulness-through-Counterfactuals, first generates a counterfactual hypothesis based logical predicates expressed in explanation, then evaluates if prediction consistent with that l...