Related papers: Translating SUMO-K to Higher-Order Set Theory
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
In this paper, we introduce a translation that combines the $j$-translation with Kripke forcing in the internal logic of an elementary topos. First, we show that our translation is sound for intuitionistic first-order logic and Heyting…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…
In this work we suggest the use of a set-theoretical interpretation of semantic tableaux for teaching propositional logic. If the student has previous notions of basic set theory, this approach to semantical tableaux can clarify her the way…
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
We present an encoding of Zermelo-Fraenkel set theory into many-sorted first-order logic, the input language of state-of-the-art SMT solvers. This translation is the main component of a back-end prover based on SMT solvers in the TLA+ Proof…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
This paper describes our submission to the First Workshop on Reordering for Statistical Machine Translation. We have decided to build a reordering system based on tree-to-string model, using only publicly available tools to accomplish this…
Conventional spoken language understanding systems consist of two main components: an automatic speech recognition module that converts audio to a transcript, and a natural language understanding module that transforms the resulting text…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…
We extend the usual internal logic of a (pre)topos to a more general interpretation, called the stack semantics, which allows for "unbounded" quantifiers ranging over the class of objects of the topos. Using well-founded relations inside…
In a previous paper, the sup-interpretation method was proposed as a new tool to control memory resources of first order functional programs with pattern matching by static analysis. Basically, a sup-interpretation provides an upper bound…
Simultaneous translation is a task in which translation begins before the speaker has finished speaking, so it is important to decide when to start the translation process. However, deciding whether to read more input words or start to…
Tuple interpretations are a class of algebraic interpretation that subsumes both polynomial and matrix interpretations as it does not impose simple termination and allows non-linear interpretations. It was developed in the context of…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…