Papers by Valeria de Paiva
Journal of Symbolic Logic, 1984
In 1965 Zadeh introduced the concept of fuzzy sets. The characteristic of fuzzy sets is that the ... more In 1965 Zadeh introduced the concept of fuzzy sets. The characteristic of fuzzy sets is that the range of truth value of the membership relation is the closed interval [0, 1] of real numbers. The logical operations ⊃, ∼ on [0, 1] which are used for Zadeh's fuzzy sets seem to be Łukasiewciz's logic, where p ⊃ q = min(1, 1 − p + q), ∼ p = 1 − p. L. S. Hay extended in [4] Łukasiewicz's logic to a predicate logic and proved its weak completeness theorem: if P is valid then P + Pn is provable for each positive integer n. She also showed that one can without losing consistency obtain completeness of the system by use of additional infinitary rule.Now, from a logical standpoint, each logic has its corresponding set theory in which each logical operation is translated into a basic operation for set theory; namely, the relation ⊆ and = on sets are translation of the logical operations → and ↔. For Łukasiewicz's logic, P Λ (P ⊃ Q). ⊃ Q is not valid. Translating it to the set v...
In this paper we consider the problem of deriving a term assignment system for Girard's Intui... more In this paper we consider the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system differs from previous calculi (e.g. that of Abramsky) and has two important properties which they lack. These are the substitution property (the set of valid deductions is closed under substitution) and subject reduction (reduction on terms is well typed). We define a simple (but more general than previous proposals) categorical model for Intuitionistic Linear Logic and show how this can be used to derive the term assignment system. We also consider term reduction arising from cut-elimination in the sequent calculus and normalisation in natural deduction. We explore the relationship between these, as well as with the equations which follow from our categorical model.
This note starts the formal study of the type system of the functional language Ponder. Some of t... more This note starts the formal study of the type system of the functional language Ponder. Some of the problems of proving soundness and completeness are discussed and some preliminary results, about fragments of the type system, shown. It consists of 6 sections. In section 1 we review briefly Ponder's syntax and describe its typing system. In section 2 we consider a very restricted fragment of the language for which we can prove soundness of the type inference mechanism, but not completeness. Section 3 describes possible models of this fragment and some related work. Section 4 describes the type-inference algorithm for a larger fragment of Ponder and in section 5 we come up against some problematic examples. Section 6 is a summary of further work.
Logic, language, information, and computation : 22nd International Workshop, WoLLIC 2015, Bloomington, IN, USA, July 20-23, 2015, proceedings Modeling Language Design for Complex Systems Simulation.- Formalization of Mathematics for Fun an... more Modeling Language Design for Complex Systems Simulation.- Formalization of Mathematics for Fun and Profit.- From Residuated Lattices via GBI-algebras to BAOs.- Towards a Nominal Chomsky Hierarchy.- Multi-Linear Algebraic Semantics for Natural Language.- Categories of Games.- Learning in the limit, general topology, and modal logic.- The Word Problem for Finitely Presented Quandles is Undecidable.- Intuitionistic Ancestral Logic as a Dependently Typed Abstract Programming Language.- On Topologically Relevant Fragments of the Logic of Linear Flows of Time.- An Equation-Based Classical Logic.- Cyclic multiplicative proof nets of linear logic with an application to language parsing.- A Dichotomy Result for Ramsey Quantifiers.- Parametric Polymorphism { Universally.- On the weak index problem for game automata.- Proof-theoretic aspects of the Lambek-Grishin Calculus.- Syllogistic Logic with "Most".- Characterizing Frame Definability in Team Semantics via The Universal Modality....
ArXiv, 2016
Lexical semantics continues to play an important role in driving research directions in NLP, with... more Lexical semantics continues to play an important role in driving research directions in NLP, with the recognition and understanding of context becoming increasingly important in delivering successful outcomes in NLP tasks. Besides traditional processing areas such as word sense and named entity disambiguation, the creation and maintenance of dictionaries, annotated corpora and resources have become cornerstones of lexical semantics research and produced a wealth of contextual information that NLP processes can exploit. New efforts both to link and construct from scratch such information - as Linked Open Data or by way of formal tools coming from logic, ontologies and automated reasoning - have increased the interoperability and accessibility of resources for lexical and computational semantics, even in those languages for which they have previously been limited. LexSem+Logics 2016 combines the 1st Workshop on Lexical Semantics for Lesser-Resources Languages and the 3rd Workshop on L...
Journal of Logic and Computation
Proceedings of the ACL-PASCAL Workshop on Textual Entailment and Paraphrasing - RTE '07, 2007
Lecture Notes in Computer Science, 2014
Lecture Notes in Computer Science, 1998
This preliminary account of our work on improving the verb lexicon of OpenWordNet-PT describes so... more This preliminary account of our work on improving the verb lexicon of OpenWordNet-PT describes some of the issues that one faces when manually cleaning up a semi-automatically constructed lexical resource and some of the lessons we learned while doing it.
Proceedings of the international conference on Formal Ontology in Information Systems - FOIS '01, 2001
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Papers by Valeria de Paiva
invited lectures and 4 tutorials, were carefully reviewed and selected from 44 submissions.
workshop itself but extending beyond it to embrace a wider range of topics related to Chu spaces and Dialectica constructions. By way of complement to Barr’s article in this issue on the conceptual evolution of
Chu spaces we offer here some prefatory remarks of our own on the nature, uses, and history of Chu spaces. We then give our perspective on where this volume’s papers fit in the overall scheme of things. Further material on Chu spaces can be found at the website http://chu.stanford.edu maintained by the second editor.