Topic
Universal quantification
About: Universal quantification is a research topic. Over the lifetime, 295 publications have been published within this topic receiving 7591 citations. The topic is also known as: for every & for all.
Papers published on a yearly basis
Papers
TL;DR: This work introduces a third, more general variety of temporal logic: alternating-time temporal logic, which offers selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves.
Abstract: Temporal logic comes in two varieties: linear-time temporal logic assumes implicit universal quantification over all paths that are generated by the execution of a system; branching-time temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general variety of temporal logic: alternating-time temporal logic offers selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves. While linear-time and branching-time logics are natural specification languages for closed systems, alternating-time logics are natural specification languages for open systems. For example, by preceding the temporal operator "eventually" with a selective path quantifier, we can specify that in the game between the system and the environment, the system has a strategy to reach a certain state. The problems of receptiveness, realizability, and controllability can be formulated as model-checking problems for alternating-time formulas. Depending on whether or not we admit arbitrary nesting of selective path quantifiers and temporal operators, we obtain the two alternating-time temporal logics ATL and ATLa.ATL and ATLa are interpreted over concurrent game structures. Every state transition of a concurrent game structure results from a choice of moves, one for each player. The players represent individual components and the environment of an open system. Concurrent game structures can capture various forms of synchronous composition for open systems, and if augmented with fairness constraints, also asynchronous composition. Over structures without fairness constraints, the model-checking complexity of ATL is linear in the size of the game structure and length of the formula, and the symbolic model-checking algorithm for CTL extends with few modifications to ATL. Over structures with weak-fairness constraints, ATL model checking requires the solution of 1-pair Rabin games, and can be done in polynomial time. Over structures with strong-fairness constraints, ATL model checking requires the solution of games with Boolean combinations of Buchi conditions, and can be done in PSPACE. In the case of ATLa, the model-checking problem is closely related to the synthesis problem for linear-time formulas, and requires doubly exponential time.
1,762 citations
Book•
1 Jan 1998TL;DR: Part 1 The modularity matching model: constraints and universal grammar the poverty of the stimulus models of language development continuity versus input matching the competing factors model compete tasks - reaction time studies competing tasks - the act-out task competing tasks and competing factors context and competing factor language processing extralinguistic knowledge.
Abstract: Part 1 The modularity matching model: constraints and universal grammar the poverty of the stimulus models of language development continuity versus input matching the competing factors model competing tasks - reaction time studies competing tasks - the act-out task competing tasks - imitation judgment tasks and competing factors context and competing factors language processing extralinguistic knowledge when principles and preferences collide performance errors methodological preliminaries. Part 2 The elicited production task: elicited production eliciting relative clauses asking questions- the "ask/tell" problem structure-dependence wanna contraction long-distance questions and the medial-wh why children make good subjects summary of designs. Part 3 The truth value judgment task: truth value judgments backward anaphora fundamentals of design: principle C what's wrong with this picture? strong crossover strongest crossover principle B following up on principle B sets and circumstances discourse binding universal quantification donkey sentences a potential drawback of the task resolving the dilemma - control sentences resolving the dilemma -varying the context.
837 citations
15 Jul 1991
TL;DR: The intuitionistic notion of context is refined by using a fragment of J.-Y.
Abstract: The intuitionistic notion of context is refined by using a fragment of J.-Y. Girard's (Theor. Comput. Sci., vol.50, p.1-102, 1987) linear logic that includes additive and multiplicative conjunction, linear implication, universal quantification, the of course exponential, and the constants for the empty context and for the erasing contexts. It is shown that the logic has a goal-directed interpretation. It is also shown that the nondeterminism that results from the need to split contexts in order to prove a multiplicative conjunction can be handled by viewing proof search as a process that takes a context, consumes part of it, and returns the rest (to be consumed elsewhere). Examples taken from theorem proving, natural language parsing, and database programming are presented: each example requires a linear, rather than intuitionistic, notion of context to be modeled adequately. >
500 citations
TL;DR: The alternating-time temporal logic (ATL) as discussed by the authors is a more general variant of temporal logic that allows selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves.
450 citations
TL;DR: The authors argue that children have full grammatical competence with universal quantification and conclude that young children are capable of producing quantificational sentences with no knowledge of any aspect of the universal quantifier.
Abstract: It is widely believed that even children as old as 4 or 5 misunderstand sentences with the universal quantifier, such as Every farmer is feeding a donkey. It is claimed that English-speaking children understand this sentence to entail that every farmer is feeding a donkey and that every donkey is being fed by a farmer. A linguistic account of the difference between children's comprehension and that of adults has recently been advanced in the literature on language acquisition within the generative framework. In this article we argue against the position that children lack knowledge of any aspect of universal quantification. We present a number of empirical and theoretical difficulties with the linguistic account of children's nonadult responses to sentences with universal quantification, and we report a series of experimental investigations of children's comprehension and production of quantificational sentences. We conclude that young children have full grammatical competence with universal quantification.
218 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 8 |
| 2020 | 5 |
| 2019 | 9 |
| 2018 | 9 |
| 2017 | 10 |
| 2016 | 8 |