Recursive First-order Syntactic Unification Modulo Variable Classes

We present a generalization of first-order syntactic unification to a term algebra where variable indexing is part of the object language. Unlike first-order syntactic unification, the number of variables within a given problem is not finitely bound as terms can have self-symmetric subterms (modulo an index shift) allowing the construction of infinitely deep terms containing infinitely many variables, what we refer to as arithmetic progressive terms. Such constructions are related to inductive reasoning. We show that unifiability is decidable for so-called simple linear 1-loops and conjecture decidability for less restricted classes of loops.Comment: pre-prin

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas

Embodiment and Grammatical Structure: An Approach to the Relation of Experience, Assertion and Truth

In this thesis I address a concern in both existential phenomenology and embodied cognition, namely, the question of how ‘higher’ cognitive abilities such as language and judgements of truth relate to embodied experience. I suggest that although our words are grounded in experience, what makes this grounding and our higher abilities possible is grammatical structure. The opening chapter contrasts the ‘situated’ approach of embodied cognition and existential phenomenology with Cartesian methodological solipsism. The latter produces a series of dualisms, including that of language and meaning, whereas the former dissolves such dualisms. The second chapter adapts Merleau-Ponty’s arguments against the perceptual constancy hypothesis in order to undermine the dualism of grammar and meaning. This raises the question of what grammar is, which is addressed in the third chapter. I acknowledge the force of Chomsky’s observation that language is structure dependent and briefly introduce a minimal grammatical operation which might be the ‘spark which lit the intellectual forest fire’ (Clark: 2001, 151). Grammatical relations are argued to make possible the grounding of our symbols in chapters 4 and 5, which attempt to ground the categories of determiner and aspect in spatial deixis and embodied motor processes respectively. Chapter 6 ties the previous three together, arguing that we may understand a given lexeme as an object or as an event by subsuming it within a determiner phrase or aspectualising it respectively. I suggest that such modification of a word’s meaning is possible because determiners and aspect schematise, i.e. determine the temporal structure, of the lexeme. Chapter 7 uses this account to take up Heidegger’s claim that the relation between being and truth be cast in terms of temporality (2006, H349), though falls short of providing a complete account of the ‘origin of truth’. Chapter 8 concludes and notes further avenues of research

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

A Critique of Western Buddhism

What are we to make of Western Buddhism? Glenn Wallis argues that in aligning their tradition with the contemporary wellness industry, Western Buddhists evade the consequences of Buddhist thought. This book shows that with concepts such as vanishing, nihility, extinction, contingency, and no-self, Buddhism, like all potent systems of thought, articulates a notion of the “real.” Raw, unflinching acceptance of this real is held by Buddhism to be at the very core of human “awakening.” Yet these preeminent human truths are universally against contemporary Buddhist practice, contravening the very heart of Buddhism

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing