Quantifiers and Cognition: Logical and Computational Perspectives

Szymanik, Jakub

doi:10.1007/978-3-319-28749-2

Cited by 45 publications

(46 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…NP-hard models of cognition pervade cognitive science, spanning many different cognitive domains, such as vision (Tsotsos 1990;van Rooij 2003), reasoning (Oaksford and Chater 1998;Levesque 1988;Reiter 1980), planning (Bylander 1994;Newell and Simon 1988), language (Barton et al 1987;Ristad 1993;Szymanik 2016;Wareham 1999) and decision-making (Otworowska et al 2017;van Rooij et al 2005). Under the P-cognition thesis it would be a natural response to disregard those models and scrape them from the list of plausible models.…”

Section: The Fpt-cognition Thesismentioning

confidence: 99%

Parameterized Complexity of Theory of Mind Reasoning in Dynamic Epistemic Logic

Pol

Rooij

Szymanik

2018

J of Log Lang and Inf

Self Cite

View full text Add to dashboard Cite

Theory of mind refers to the human capacity for reasoning about others' mental states based on observations of their actions and unfolding events. This type of reasoning is notorious in the cognitive science literature for its presumed computational intractability. A possible reason could be that it may involve higher-order thinking (e.g., 'you believe that I believe that you believe'). To investigate this we formalize theory of mind reasoning as updating of beliefs about beliefs using dynamic epistemic logic, as this formalism allows to parameterize 'order of thinking.' We prove that theory of mind reasoning, so formalized, indeed is intractable (specifically, PSPACE-complete). Using parameterized complexity we prove, however, that the 'order parameter' is not a source of intractability. We furthermore consider a set of alternative parameters and investigate which of them are sources of intractability. We discuss the implications of these results for the understanding of theory of mind.

show abstract

Section: The Fpt-cognition Thesismentioning

confidence: 99%

Parameterized Complexity of Theory of Mind Reasoning in Dynamic Epistemic Logic

Pol

Rooij

Szymanik

2018

J of Log Lang and Inf

Self Cite

View full text Add to dashboard Cite

show abstract

“…The evolutionary process and rationality are thought to ensure that human cognitive acts are generally optimized for the task and thus the focus can be on the computational level of explanation. As cognitive scientists have developed the computational modeling of cognitive tasks, the focus has indeed moved to the computational level more than to the algorithmic and implementation levels (see, e.g., Isaac et al 2014;Szymanik 2016; for a recent example, see Piantadosi et al 2016). 4 In this paper, I call the approach that combines computational-level explanations with results from computational complexity theory the computational complexity approach to cognitive complexity.…”

Section: What Is Cognitive Complexity?mentioning

confidence: 99%

Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving

Pantsar

2019

Erkenn

View full text Add to dashboard Cite

Following Marr's famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that the complexity of the task of solving a problem can be characterized by the computational complexity of that problem. In this paper, I argue that human cognizers use heuristic and didactic tools and thus engage in cognitive processes that make their problem solving algorithms computationally suboptimal, in contrast with the optimal algorithms studied in the computational approach. Therefore, in order to accurately model the human cognitive tasks involved in mathematical problem solving, we need to expand our methodology to also include aspects relevant to the algorithmic level. This allows us to study algorithms that are cognitively optimal for human problem solvers. Since problem solving methods are not universal, I propose that they should be studied in the framework of enculturation, which can explain the expected cultural variance in the humanly optimal algorithms. While mathematical problem solving is used as the case study, the considerations in this paper concern modeling of cognitive tasks in general.

show abstract

“…Here, verification is a task in which a human subject tries to recognize the truth value of a sentence in a given context. Using cognitively plausible measures of complexity, we can distinguish between meanings which are easy and hard to verify (see, also, Szymanik 2016).…”

Section: Computational Complexity and Cognitionmentioning

confidence: 99%

“…van Lambalgen and Hamm (2005) consider a cognitively motivated approach to the semantics of tense aspect and nominalization. Suppes (1980Suppes ( , 1982 claims that there are psychological reasons for scrutinising semantics of everyday expressions in terms of associations between linguistic constructions and procedures which get activated during language use [see Szymanik (2016) for a broader discussion on this topic]. As a matter of fact, empirical studies suggest that linguistic constructions are associated with specific procedures (Pietroski et al 2009;Lidz et al 2011;Tomaszewicz 2013).…”

Section: Introductionmentioning

confidence: 99%

Semantics of the Barwise sentence: insights from expressiveness, complexity and inference

Kalociński

Godziszewski

2018

Linguist and Philos

View full text Add to dashboard Cite

In this paper, we study natural language constructions which were first examined by Barwise: The richer the country, the more powerful some of its officials. Guided by Barwise's observations, we suggest that conceivable interpretations of such constructions express the existence of various similarities between partial orders such as homomorphism or embedding (strong readings). Semantically, we interpret the constructions as polyadic generalized quantifiers restricted to finite models (similarity quantifiers). We extend the results obtained by Barwise by showing that similarity quantifiers are not expressible in elementary logic over finite models. We also investigate whether the proposed readings are sound from the cognitive perspective. We prove that almost all similarity quantifiers are intractable. This leads us to first-order variants (weak readings), which only approximate the strong readings, but are cognitively more plausible. Driven by the question of ambiguity, we recall Barwise's argumentation in favour of strong readings, enriching it with some arguments of our own. Given that Barwise-like sentences are indeed ambiguous, we use a generalized Strong Meaning Hypothesis to derive predictions for their verification. Finally, we propose a hypothesis according to which conflicting pressures of communication and cognition might give rise to an ambiguous construction, provided that different semantic variants of the construction withstand different pressures involved in its usage.

show abstract

Quantifiers and Cognition: Logical and Computational Perspectives

Cited by 45 publications

References 0 publications

Parameterized Complexity of Theory of Mind Reasoning in Dynamic Epistemic Logic

Parameterized Complexity of Theory of Mind Reasoning in Dynamic Epistemic Logic

Cognitive and Computational Complexity: Considerations from Mathematical Problem Solving

Semantics of the Barwise sentence: insights from expressiveness, complexity and inference

Contact Info

Product

Resources

About