Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative (...) ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis. (shrink)

We overview logical and computational explanations of the notion of tractability as applied in cognitive science. We start by introducing the basics of mathematical theories of complexity: computability theory, computational complexity theory, and descriptive complexity theory. Computational philosophy of mind often identifies mental algorithms with computable functions. However, with the development of programming practice it has become apparent that for some computable problems finding effective algorithms is hardly possible. Some problems need too much computational resource, e.g., time or memory, to (...) be practically computable. Computational complexity theory is concerned with the amount of resources required for the execution of algorithms and, hence, the inherent difficulty of computational problems. An important goal of computational complexity theory is to categorize computational problems via complexity classes, and in particular, to identify efficiently solvable problems and draw a line between tractability and intractability. -/- We survey how complexity can be used to study computational plausibility of cognitive theories. We especially emphasize methodological and mathematical assumptions behind applying complexity theory in cognitive science. We pay special attention to the examples of applying logical and computational complexity toolbox in different domains of cognitive science. We focus mostly on theoretical and experimental research in psycholinguistics and social cognition. (shrink)

Book Description (Blurb): Cognitive Design for Artificial Minds explains the crucial role that human cognition research plays in the design and realization of artificial intelligence systems, illustrating the steps necessary for the design of artificial models of cognition. It bridges the gap between the theoretical, experimental and technological issues addressed in the context of AI of cognitive inspiration and computational cognitive science. -/- Beginning with an overview of the historical, methodological and technical issues in the field of Cognitively-Inspired Artificial Intelligence, (...) Lieto illustrates how the cognitive design approach has an important role to play in the development of intelligent AI technologies and plausible computational models of cognition. Introducing a unique perspective that draws upon Cybernetics and early AI principles, Lieto emphasizes the need for an equivalence between cognitive processes and implemented AI procedures, in order to realise biologically and cognitively inspired artificial minds. He also introduces the Minimal Cognitive Grid, a pragmatic method to rank the different degrees of biologically and cognitive accuracy of artificial systems in order project and predict their explanatory power with respect to the natural systems taken as source of inspiration. -/- Providing a comprehensive overview of cognitive design principles in constructing artificial minds, this text will be essential reading for students and researchers of artificial intelligence and cognitive science. (shrink)

The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance theTractable Cognition thesis: Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constraining the space of computational‐level theories of cognition. To utilize this constraint, a precise and workable definition of “computational tractability” is needed. Following computer science tradition, many cognitive scientists and psychologists define computational tractability as polynomial‐time computability, leading to theP‐Cognition thesis. This article (...) explains how and why the P‐Cognition thesis may be overly restrictive, risking the exclusion of veridical computational‐level theories from scientific investigation. An argument is made to replace the P‐Cognition thesis by theFPT‐Cognition thesisas an alternative formalization of the Tractable Cognition thesis (here, FPT stands for fixed‐parameter tractable). Possible objections to the Tractable Cognition thesis, and its proposed formalization, are discussed, and existing misconceptions are clarified. (shrink)

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. 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. 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. (shrink)

We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. Next, we focus on a linguistic case study. We use computational complexity results to investigate semantic (...) distinctions between quantified reciprocal sentences. We show a computational dichotomy<br>between different readings of reciprocity. Finally, we go more into philosophical speculation on meaning, ambiguity and computational complexity. In particular, we investigate a possibility to<br>revise the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multi-quantifier sentences. The paper not only contributes to the field of the formal<br>semantics but also illustrates how the tools of computational complexity theory might be successfully used in linguistics and philosophy with an eye towards cognitive science. (shrink)

We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality.<br>In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and push-down automata is psychologically relevant. Our research improves upon hypothesis and (...) explanatory power of recent neuroimaging studies as well as provides<br>evidence. (shrink)

We report two experiments which tested whether cognitive capacities are limited to those functions that are computationally tractable (PTIME-Cognition Hypothesis). In particular, we investigated the semantic processing of reciprocal sentences with generalized quantifiers, i.e., sentences of the form Q dots are directly connected to each other, where Q stands for a generalized quantifier, e.g. all or most. Sentences of this type are notoriously ambiguous and it has been claimed in the semantic literature that the logically strongest reading is preferred (Strongest (...) Meaning Hypothesis). Depending on the quantifier, the verification of their strongest interpretations is computationally intractable whereas the verification of the weaker readings is tractable. We conducted a picture completion experiment and a picture verification experiment to investigate whether comprehenders shift from an intractable reading to a tractable reading which should be dispreferred according to the Strongest Meaning Hypothesis. The results from the picture completion experiment suggest that intractable readings occur in language comprehension. Their verification, however, rapidly exceeds cognitive capacities in case the verification problem cannot be solved using simple heuristics. In particular, we argue that during verification, guessing strategies are used to reduce computational complexity. (shrink)

Many cognitive scientists, having discovered that some computational-level characterization f of a cognitive capacity φ is intractable, invoke heuristics as algorithmic-level explanations of how cognizers compute f. We argue that such explanations are actually dysfunctional, and rebut five possible objections. We then propose computational-level theory revision as a principled and workable alternative.

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

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. (shrink)

We consider the notion of everyday language. We claim that everyday language is semantically bounded by the properties expressible in the existential fragment of second–order logic. Two arguments for this thesis are formulated. Firstly, we show that so–called Barwise's test of negation normality works properly only when assuming our main thesis. Secondly, we discuss the argument from practical computability for finite universes. Everyday language sentences are directly or indirectly verifiable. We show that in both cases they are bounded by second–order (...) existential properties. Moreover, there are known examples of everyday language sentences which are the most difficult in this class (NPTIME–complete). (shrink)

In this paper, I argue that computationalism is a progressive research tradition. Its metaphysical assumptions are that nervous systems are computational, and that information processing is necessary for cognition to occur. First, the primary reasons why information processing should explain cognition are reviewed. Then I argue that early formulations of these reasons are outdated. However, by relying on the mechanistic account of physical computation, they can be recast in a compelling way. Next, I contrast two computational models of working memory (...) to show how modeling has progressed over the years. The methodological assumptions of new modeling work are best understood in the mechanistic framework, which is evidenced by the way in which models are empirically validated. Moreover, the methodological and theoretical progress in computational neuroscience vindicates the new mechanistic approach to explanation, which, at the same time, justifies the best practices of computational modeling. Overall, computational modeling is deservedly successful in cognitive science. Its successes are related to deep conceptual connections between cognition and computation. Computationalism is not only here to stay, it becomes stronger every year. (shrink)

One of the critical issues in the philosophy of science is to understand scientific knowledge. This paper proposes a novel approach to the study of reflection on science, called “cognitive metascience”. In particular, it offers a new understanding of scientific knowledge as constituted by various kinds of scientific representations, framed as cognitive artifacts. It introduces a novel functional taxonomy of cognitive artifacts prevalent in scientific practice, covering a huge diversity of their formats, vehicles, and functions. As a consequence, toolboxes, conceptual (...) frameworks, theories, models, and individual hypotheses can be understood as artifacts supporting our cognitive performance. It is also shown that by empirically studying how artifacts function, we may discover hitherto undiscussed virtues and vices of these scientific representations. This paper relies on the use of language technology to analyze scientific discourse empirically, which allows us to uncover the metascientific views of researchers. This, in turn, can become part of normative considerations concerning virtues and vices of cognitive artifacts. (shrink)

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. Semantically, we interpret the constructions as polyadic generalized quantifiers restricted to finite models. 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, 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. (shrink)

Single cell recordings in monkeys provide strong evidence for an important role of the motor system in action understanding. This evidence is backed up by data from studies of the (human) mirror neuron system using neuroimaging or TMS techniques, and behavioral experiments. Although the data acquired from single cell recordings are generally considered to be robust, several debates have shown that the interpretation of these data is far from straightforward. We will show that research based on single-cell recordings allows for (...) unlimited content attribution to mirror neurons. We will argue that a theoretical analysis of the mirroring process, combined with behavioral and brain studies, can provide the necessary limitations. A complexity analysis of the type of processing attributed to the mirror neuron system can help formulate restrictions on what mirroring is and what cognitive functions could, in principle, be explained by a mirror mechanism. We argue that processing at higher levels of abstraction needs assistance of non-mirroring processes to such an extent that subsuming the processes needed to infer goals from actions under the label ?mirroring? is not warranted. (shrink)

Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.

A central aim of cognitive science is to understand the fundamental mechanisms that enable humans to navigate and make sense of complex environments. In this letter, we argue that computational complexity theory, a foundational framework for evaluating computational resource requirements, holds significant potential in addressing this challenge. As humans possess limited cognitive resources for processing vast amounts of information, understanding how humans perform complex cognitive tasks requires comprehending the underlying factors that drive information processing demands. Computational complexity theory provides a (...) comprehensive theoretical framework to achieve this goal. By adopting this framework, we can gain new insights into how cognitive systems work and develop a more nuanced understanding of the relation between task complexity and human behavior. We provide empirical evidence supporting our argument and identify several open research questions and challenges in applying computational complexity theory to human decision‐making and cognitive science at large. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...) computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)

In light of the recent credibility crisis in psychology, this paper argues for a greater emphasis on theorizing in scientific research. Although reliable experimental evidence, preregistration, methodological rigor, and new computational frameworks for modeling are important, scientific progress also relies on properly functioning theories. However, the current understanding of the role of theorizing in psychology is lacking, which may lead to future crises. Theories should not be viewed as mere speculations or simple inductive generalizations. To address this issue, the author (...) introduces a framework called “cognitive metascience,” which studies the processes and results of evaluating scientific practice. This study should proceed both qualitatively, as in traditional science and technology studies and cognitive science, and quantitatively, by analyzing scientific discourse using language technology. By analyzing theories as cognitive artifacts that support cognitive tasks, this paper aims to shed more light on their nature. This perspective reveals that multiple distinct theories serve entirely different roles, and studying these roles, along with their epistemic vices and virtues, can provide insight into how theorizing should proceed. The author urges a change in research culture to appreciate the variety of distinct theories and to systematically advance scientific progress. . (shrink)

Contemporary psychologism has been amended for most of the objections by its opponents over a century ago. However, some authors still raise doubts about its ability to account for some peculiar properties of logic. In particular, it is argued that the psychological universality of patterns of inferential behavior is not sufficient to account for the normativity of logic. In this paper, I deal with the issue and offer three alternative solutions that do not rely on mere empirical universality. I will (...) use the works of Laurence Jonathan Cohen, Diego Marconi and Marcello D'Agostino, adapting them for the purpose of defending logical psychologism. I will therefore argue that, although more refined work on the subject is needed, contemporary psychologism has the key resources to retain its place in the philosophical debate on the foundations of logic. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

In this paper, I will discuss a well-known oscillation in Frege’s conception of sense. My point is only partially concerned with his two different criteria of sense identity, and touches upon a more specific point: what happens if we apply Frege’s intuitive criterion for the difference of thoughts to logically equivalent sentences? I will try to make a schematic argument here that will preempt any endeavor to make Frege more coherent than he really is. In sections A and B, I (...) will present two alternative Fregean ways to treat the sense of logically equivalent sentences. Frege really oscillated between two alternative conceptions of sense, and his inability to detect the contrast between the two alternative conceptions is partly due to his strong conception of rationality. To apply the criterion of difference of thoughts to logical matters, we may also use a weak notion of rationality, or at least a notion of rationality of human agents, with limited computational resources. The distinctions towards which Frege was striving are better understood nowadays from the point of view of the treatment of limited rationality, which imposes itself even in logical matters. (shrink)