Much effort has been devoted in the past decade to the development of decision procedures for quantified Boolean formulas (QBFs) in order to improve their performance. Besides solving the decision problem of whether a closed QBF is true and returning yes or no, modern QBF solvers can produce clause or cube proofs to certify their answer. These proofs can be used to derive solutions to problems ...

We will not prove the theorem here, but we should step back and take a minute to think about the meaning of this theorem. A naive NL algorithm for Conn is to take the same NTM for Conn but flip its answers. Thus, we will accept, if there exists a wrong guess connecting s to t. However, for any (s, t), there exists a wrong guess, and we will end up accepting everything! Essentially, if (G, s, t)...

Classical quantifiers (e.g., “all”, “some” and “none”) have been extensively studied in logic and psychology. In contrast, generalized quantifiers (e.g., “most”) allow for fine-grained statements about quantities. The discrepancy in the underlying mental representation and its interpretation among interpreters can affect language use and reasoning. We investigated the effect of quantifier type,...

When analyzing database query languages a property of theories, the pseudo-finite homogeneity property has been introduced and applied (cf. [3]). We show that a stable theory has the pseudo-finite homogeneity property just in case its expressive power for finite states is bounded. Moreover, we introduce the corresponding pseudo-finite saturation property and show that a theory fails to have the...

We present a layered bit-blasting-free algorithm for existentially quantifying variables from conjunctions of linear modular (bitvector) equations (LMEs) and disequations (LMDs). We then extend our algorithm to work with arbitrary Boolean combinations of LMEs and LMDs using two approaches – one based on decision diagrams and the other based on SMT solving. Our experiments establish conclusively...

It was considered to be “typical for first order theories” that a restriction to sentences with only a limited number of quantilier alternations leads to an exponential decrease of complexity. Using domino games, which were treated in a previous paper to describe computations of alternating Turing machines, we prove that this is not always true. We present a list of theories, all of them decida...

Quantifier reasoning in Satisfiability Modulo Theories (SMT) is a long-standing challenge. The practical method employed in modern SMT solvers is to instantiate quantified formulas based on heuristics, which is not refutationally complete even for pure first-order logic. We present several decidable fragments of first order logic modulo theories. We show how to construct models for satisfiable ...

Since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them, linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning. This paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures,...

Abstract Can conjunctive propositions be identical without their conjuncts being identical? universally quantified instances On a common conception of propositions, on which they inherit the logical structure sentences express them, answer is negative both times. Here, it will shown that such to questions inconsistent, assuming standard type-theoretic formalization theorizing about propositions...

Downward entailing linguistic environments license inferences from sets to their subsets. These environments also determine the interpretation of disjunction: Disjunction licenses a conjunctive entailment in the scope of downward entailing operators (Crain 2008, 2012). This leads to a striking asymmetry across languages in the interpretation of disjunction when it appears in the restrictor (dow...