In this paper I draw from Martin Heidegger’s phenomenology of the 1920s to outline some basic features of his theory of intentionality that I believe have not been fully appreciated or utilized, and that allow for both novel and fruitful interventions in questions about meaning, the relationship between mind and the world, and epistemic justification, principally as they appear in John McDowell’s synoptic project in Mind and World. I argue that while elements of McDowell’s picture are ultimately unsatisfying and problematic, (...) much of his conceptual framework can and should be put into dialogue with Heidegger’s, and that in so doing we make available powerful resources for amending the McDowellian account. Moreover, these emendations have attractive implications for his distinctive desiderata. In particular, they provide original conceptions of normativity’s place in nature, of the boundaries of the space of reasons, and of the relationship between the answerability of thought both to the world and to human beings as a rational community. (shrink)

The AGM paradigm for belief revision provides a very elegant and powerful framework for reasoning about idealized agents. The paradigm assumes that the modeled agent is a perfect reasoner with infinite memory. In this paper we propose a framework to reason about non-ideal agents that generalizes the AGM paradigm. We first introduce a structure to represent an agent's belief states that distinguishes different status of beliefs according to whether or not they are explicitly represented, whether they are currently active (...) and whether they are fully accepted or provisional. Then we define a set of basic operations that change the status of beliefs and show how these operations can be used to model agents with different capacities. We also show how different operations of belief change described in the literature can be seen as special cases of our theory. (shrink)

Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, G¨ardenfors and Makinson (AGM) [1] describes postulates which a rational belief revision and contraction operations should satisfy. The AGM postulates have been perceived (...) as characterising idealised rational reasoners, and the corresponding belief change operations are considered unsuitable for implementable agents due to their high computational cost [3]. The main result of this paper is showing that an efficient (linear time) belief contraction operation nevertheless satisfies all but one of the AGM postulates for contraction. This contraction operation is defined for a realistic rule-based agent which can be seen as a reasoner in a very weak logic; although the agent’s beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of contraction for our agent. (shrink)

We introduce a three-tiered framework for modelling and reasoning about agents who (i) can use possibly complete reasoning systems without any restrictions but who nevertheless are (ii) bounded in the sense that they never reach infinitely many results and, finally, who (iii) perform their reasoning in time. This last aspect does not concern so much the time it takes for agents to actually carry out their reasoning, as the time which can bring about external changes (...) in the agents’ states such as arriving of new information or discarding previously available information due to bounds of the agent’s resources. These three aspects are treated with the maximal possible degree of independence from each other. The treatment of layer (iii) can be combined with arbitrary logic at level (ii) which, in turn, can be combined with arbitrary agent logic at level (i). At the level (iii), we discuss briefly the duality (or rather, complementarity) of system descriptions based on actions and transitions, on the one hand, and states and their changes, on the other. We settle for the latter and present a simple language, for describing state changes, which is parameterized by an arbitrary language for describing properties of the states. The language can be viewed as a simple fragment of step logic, admitting however various extensions by appropriate choices of the underlying logic. Alternatively, it can be seen as a very specific fragment of temporal logic (with a variant of ‘until’ or ‘chop’ operator), and is interpreted over dense linear time. The reasoning system presented here is sound, as well as strongly complete and decidable (provided that so is the parameter logic for reasoning about single states). We give the main idea of the completeness proof and suggest a wide range of possible applications, which is a simple consequence of the parametric character of both the language and the reasoning system. We address then in more detail the case of non-omniscient rational agents, (ii). Their models are syntactic structures (sets of available formulae) similar in spirit, though not in the technical formulation, to the models used in other syntax oriented approaches and in active logic. We give a new sound, complete and decidable system for reasoning about such agents. Finally, we illustrate its extensions with the internal reasoning of agents, (i), by equipping them with some example logics. (shrink)

Classical propositional logic plays a prominent role in industrial applications, and yet the complexity of this logic is presumed to be non-feasible. Tractable systems such as depth-bounded boolean logics approximate classical logic and can be seen as a model for resource-bounded agents whose reasoning style is nonetheless classical. In this paper we first study a hierarchy of tractable logics that is not defined by depth. Then we extend it into a modal logic where modalities make explicit (...) the assumptions discharged in propositional proofs, thereby expressing blueprints for proofs. A natural deduction system is provided that permits to reason about and manage such proof blueprints. (shrink)

The paper presents a new logic for reasoning about the formation of beliefs through perception or through inference in non-omniscient resource-bounded agents. The logic distinguishes the concept of explicit belief from the concept of background knowledge. This distinction is reflected in its formal semantics and axiomatics: we use a non-standard semantics putting together a neighborhood semantics for explicit beliefs and relational semantics for background knowledge, and we have specific axioms in the logic highlighting the relationship between the (...) two concepts. Mental operations of perceptive type and inferential type, having effects on epistemic states of agents, are primitives in the object language of the logic. At the semantic level, they are modelled as special kinds of model-update operations, in the style of dynamic epistemic logic. Results about axiomatization, decidability and complexity for the logic are given in the paper. (shrink)

Many problems in Multi-Agent Systems (MASs) research are formulated in terms of the abilities of a coalition of agents. Existing approaches to reasoning about coalitional ability are usually focused on games or transition systems, which are described in terms of states and actions. Such approaches however often neglect a key feature of multi-agent systems, namely that the actions of the agents require resources. In this paper, we describe a logic for reasoning about coalitional ability under resource constraints (...) in the probabilistic setting. We extend Resource-bounded Alternating-time Temporal Logic (RB-ATL) with probabilistic reasoning and provide a standard algorithm for the model-checking problem of the resulting logic Probabilistic resource-bounded ATL (pRB-ATL). We implement model-checking algorithms and present experimental results using simple multi-agent model-checking problems of increasing complexity. (shrink)

The effective reasoning capability of an agent can be defined as its capability to infer, within a given space and time bound, facts that are logical consequences of its knowledge base. In this paper we show how to determine the effective reasoning capability of an agent with limited memory by encoding the agent as a transition system and automatically verifying whether a state where the agent believes a certain conclusion is reachable from the start state. We present experimental (...) results using the Model Based Planner (MBP) which illustrates how the length of the deduction varies for different memory sizes. (shrink)

There exists a considerable body of work on epistemic logics for resource-bounded reasoners. In this paper, we concentrate on a less studied aspect of resource-bounded reasoning, namely, on the ascription of beliefs and inference rules by the agents to each other. We present a formal model of a system of bounded reasoners which reason about each other’s beliefs, and investigate the problem of belief ascription in a resource-bounded setting. We show that for (...) agents whose computational resources and memory are bounded, correct ascription of beliefs cannot be guaranteed, even in the limit. We propose a solution to the problem of correct belief ascription for feasible agents which involves ascribing reasoning strategies , or preferences on formulas, to other agents, and show that if a resource-bounded agent knows the reasoning strategy of another agent, then its ascription of beliefs to the other agent is correct in the limit. (shrink)

Previous theory and research on bounded rationality has emphasized how limited cognitive resources constrain people from making utility maximizing choices. This paper expands the concept of bounded rationality to consider how people’s rationality may be constrained by their internalization of a qualitatively distinct standard for sound judgment, which is commonly labeled reasonableness. In contrast to rationality, the standard of reasonableness provides guidance for making choices in situations that involve balancing incommensurable values and interests or reconciling conflicting points-of-view. We (...) review recent evidence showing that laypeople readily recognize the distinctions between rationality and reasonableness and thus are able to utilize these as distinct standards to inform their everyday decision-making. The fact that people appear to have internalized rationality and reasonableness as distinct standards of sound judgment supports the notion that people’s pursuit of rationality may be bounded by their determination to also be reasonable. (shrink)

Many formalisms for reasoning about knowing commit an agent to be logically omniscient. Logical omniscience is an unrealistic principle for us to use to build a real-world agent, since it commits the agent to knowing infinitely many things. A number of formalizations of knowledge have been developed that do not ascribe logical omniscience to agents. With few exceptions, these approaches are modifications of the possible-worlds semantics. In this paper we use a combination of several general techniques for building non-omniscient (...) reasoners. First we provide for the explicit representation of notions such as problems, solutions, and problem solving activities, notions which are usually left implicit in the discussions of autonomous agents. A second technique is to take explicitly into account the notion of resource when we formalize reasoning principles. We use the notion of resource to describe interesting principles of reasoning that are used for ascribing knowledge to agents. For us, resources are abstract objects. We make extensive use of ordering and inaccessibility relations on resources, but we do not find it necessary to define a metric. Using principles about resources without using a metric is one of the strengths of our approach.We describe the architecture of a reasoner, built from a finite number of components, who solves a puzzle, involving reasoning about knowing, by explicitly using the notion of resource. Our approach allows the use of axioms about belief ordinarily used in problem solving – such as axiom K of modal logic – without being forced to attribute logical omniscience to any agent. In particular we address the issue of how we can use resource-unbounded (e.g., logically omniscient) reasoning to attribute knowledge to others without introducing contradictions. We do this by showing how omniscient reasoning can be introduced as a conservative extension over resource-bounded reasoning. (shrink)

In this paper we design a new logical system to explicitly model the different deductive reasoning steps of a boundedly rational agent. We present an adequate system in line with experimental findings about an agent’s reasoning limitations and the cognitive effort that is involved. Inspired by Dynamic Epistemic Logic, we work with dynamic operators denoting explicit applications of inference rules in our logical language. Our models are supplemented by (a) impossible worlds (not closed under logical consequence), suitably structured (...) according to the effect of inference rules, and (b) quantitative components capturing the agent’s cognitive capacity and the cognitive costs of rules with respect to certain resources (e.g. memory, time). These ingredients allow us to avoid problematic logical closure principles, while at the same time deductive reasoning is reflected in our dynamic truth clauses. We further show that our models can be reduced to awareness-like plausibility structures that validate the same formulas and we give a sound and complete axiomatization with respect to them. This approach to the agent’s internal deductive reasoning is finally combined with actions of external information. (shrink)

We present a framework for verifying systems composed of heterogeneous reasoning agents, in which each agent may have differing knowledge and inferential capabilities, and where the resources each agent is prepared to commit to a goal (time, memory and communication bandwidth) are bounded. The framework allows us to investigate, for example, whether a goal can be achieved if a particular agent, perhaps possessing key information or inferential capabilities, is unable (or unwilling) to contribute more than a given portion (...) of its available computational resources or bandwidth to the problem. We present a novel temporal epistemic logic, BMCL-CTL , which allows us to describe a set of reasoning agents with bounds on time, memory and the number of messages they can exchange. The bounds on memory and communication are expressed as axioms in the logic. As an example, we show how to axiomatise a system of agents which reason using resolution and prove that the resulting logic is sound and complete. We then show how to encode a simple system of reasoning agents specified in BMCL-CTL in the description language of the Mocha model checker (Alur et al., Proceedings of the tenth international conference on computer-aided verification (CAV) , 1998), and verify that the agents can achieve a goal only if they are prepared to commit certain time, memory and communication resources. (shrink)

There is much to appreciate in Samuel Fleischacker’s Divine Teaching and the Way of the World: A Defense of Revealed Religion. In the tradition of Tolstoy, Fleischacker argues that secular philosophy does not have the resources to provide for a meaningful life; a life of meaning is to be found principally through revealed religion. In the end, however, his concept of revelation seems very thin, ruling out even the intelligibility of experiencing God. We critically assess his atrophied concept of revelation (...) and his views on historical truth, science, and theism. (shrink)

We introduce a “reason-based” framework for explaining and predicting individual choices. It captures the idea that a decision-maker focuses on some but not all properties of the options and chooses an option whose motivationally salient properties he/she most prefers. Reason-based explanations allow us to distinguish between two kinds of context-dependent choice: the motivationally salient properties may (i) vary across choice contexts, and (ii) include not only “intrinsic” properties of the options, but also “context-related” properties. Our framework can accommodate boundedly rational (...) and sophisticatedly rational choice. Since properties can be recombined in new ways, it also offers resources for predicting choices in unobserved contexts. (shrink)

We study the logic of strategic ability of coalitions of agents with bounded memory by introducing Alternating-time Temporal Logic with Bounded Memory (ATLBM), a variant of Alternating-time Temporal Logic (ATL). ATLBM accounts for two main consequences of the assumption that agents have bounded memory. First, an agent can only remember a strategy that specifies actions in a bounded number of different circumstances. While the ATL-formula means that coalition C has a joint strategy which will make φ (...) true forever, the ATLBM-formula means that C has a joint strategy which for each agent in C specifies what to do in no more than n different circumstances and which will make φ true forever. Second, an agent has bounded recall—a strategy can only take the last m states of the system into account. We use the logic to study the interaction between strategic ability, bounded number of decisions, bounded recall and incomplete information. We discuss the logical properties and expressiveness of ATLBM, and its relationship to ATL. We show that ATLBM can express properties of strategic ability under bounded memory which cannot be expressed in ATL. (shrink)

While game theory has been transformative for decision making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-k reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model called the quantal hierarchy model, which can relax both mutual consistency and best response while still approximating (...) level-k, QRE, or typical Nash equilibrium behavior in the limiting cases. The model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decision-making in extensive-form game tree. This representation enables us to treat simultaneous games in a similar manner to sequential games, where reasoning resources deplete throughout the game-tree. Bounds in player processing abilities are captured as information costs, where future branches of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the effectiveness of the quantal hierarchy model in several canonical economic games, both simultaneous and sequential, using out-of-sample modelling. (shrink)

We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the participants who (...) classified the formula correctly before timeout and the mean response time among those participants. We propose a new proof formalism for modeling propositional reasoning with bounded cognitive resources. It models declarative memory, visual memory, working memory, and procedural memory according to the memory model of Atkinson and Shiffrin and reasoning processes according to the model of Newell and Simon. We also define two particular proof systems, T and NT, for showing propositional formulas to be tautologies and non-tautologies, respectively. The accuracy was found to be higher for non-tautologies than for tautologies ( p T was.89 and for non-tautologies the correlation between latency and minimum proof length in NT was.87. (shrink)

All forms of cognition, whether natural or artificial, are subject to constraints of their computing architecture. This assumption forms the tenet of virtually all general theories of cognition, including those deriving from bounded optimality and bounded rationality. In this letter, we highlight an unresolved puzzle related to this premise: what are these constraints, and why are cognitive architectures subject to cognitive constraints in the first place? First, we lay out some pieces along the puzzle edge, such as computational (...) tradeoffs inherent to neural architectures that give rise to rational bounds of cognition. We then outline critical next steps for characterizing cognitive bounds, proposing that some of these bounds can be subject to modification by cognition and, as such, are part of what is being optimized when cognitive agents decide how to allocate cognitive resources. We conclude that these emerging views may contribute to a more holistic perspective on the nature of cognitive bounds, as well as their alteration subject to cognition. (shrink)

Defeasible reasoning is concerned with the logics of non-deductive argument. As is described in the literature, the study of this type of reasoning is considerably more involved than the study of deductive argument, even so that, in realistic applications, there is often a lack of resources to perform an exhaustive analysis. It follows that, in a theory of defeasible reasoning, the order and direction in which arguments are developed, i.e. theprocedure, is important. The aim of this article (...) is to show that debate is the most efficient procedure to argue in the presence of limited resources. To do so, there is first some general theory on defeasible argumentation, which is followed by an introduction to the problem of dialectical search. The problem of dialectical search is (or at least, should be) the essential issue in every theory on argumentation, and emerges at every occasion that involves adjudication on competing arguments. Starting with an example, it is explained that dialectical search can be best scheduled according to classical debating techniques, that work along well-tried methods. These methods (which include various forms of curtailment, interruption, and interpretation) have proven their value in keeping debating efforts within reasonable bounds. How they apply in a theory of formal argument, will be shown in this article. (shrink)

To express fine-grained resource-sensitive reasoning, a temporal soft linear logic (TSLL) is introduced as an extension of both Girard's (propositional classical) linear logic (CLL) and Lafont's (propositional classical) soft linear logic (SLL). It is known that the linear exponential operator in CLL can express a specific infinitely reusable resource, i.e. it is reusable not only for any number, but also many times. In contrast, the soft exponential operator in SLL, which is a weak version of the linear (...) exponential operator, can express a specific usable resource, i.e. it is usable in any number, but only once (i.e. it is consumed after use). In TSLL, the resource operators (i.e. linear and soft exponentials) and some temporal operators are combined based on the interpretation that “time” is regarded as a “resource”. The completeness theorem (with respect to phase semantics) for TSLL and the cut-elimination and decidability theorems for some subsystems of TSLL are proved as the main results of this paper. A decidable subsystem, called a bounded soft linear logic (BSLL), which has a restricted soft exponential operator, can represent a specific finitely usable resource. (shrink)

This paper presents an attempt to bridge the gap between logical and cognitive treatments of strategic reasoning in games. There have been extensive formal debates about the merits of the principle of backward induction among game theorists and logicians. Experimental economists and psychologists have shown that human subjects, perhaps due to their bounded resources, do not always follow the backward induction strategy, leading to unexpected outcomes. Recently, based on an eye-tracking study, it has turned out that even human (...) subjects who produce the outwardly correct ‘backward induction answer’ use a different internal reasoning strategy to achieve it. The paper presents a formal language to represent different strategies on a finer-grained level than was possible before. The language and its semantics help to precisely distinguish different cognitive reasoning strategies, that can then be tested on the basis of computational cognitive models and experiments with human subjects. The syntactic framework of the formal system provides a generic way of constructing computational cognitive models of the participants of the Marble Drop game. (shrink)

In this chapter, I examine the concept of vulnerability as a complex constitutive feature of human agency and argue that it is both a constraint on and a resource for practical reasoning. When discussed as an ontological feature of human agency, vulnerability is primarily understood as an aspect of embodiment, which is problematic in different respects. First, in relation to the situatedness of human agency, vulnerability indicates that human agents are subjected to contextual contingencies. Second, in relation to (...) temporality, vulnerability indicates that agents act in time and under the pressure of time. They are finite and produce finite and perishable actions, even though the longlasting effects of an action may survive the action itself. Third, in relation to corporal feature of agency, vulnerability is associated to suffering and frailty, insofar as bodily needs and desires represent both springs of and hindrances to rational action. Finally, in relation to the social nature of human animals, vulnerability indicates the susceptibility to be harmed, obstructed, undercut or manipulated by other agents These varieties of vulnerability are constituive features of human agency, which cannot be removed without removing what is peculiar and specific to human agency. Theories of practical reason are primarily concerned with constitutive vulnerability as a defect, and presume to offer normative guidance by adopting an idealized account of rational agency, which corrects or merely cancels the defective features of human agency. By contrast, theories of bounded rationality understand practical reasoning instrumentally, and thus are concerned with cognitive limitations of practical rationality, in particular with partial and perspectival information. However, the notion of “partial information” is inadequate to capture the complexities and significance of vulnerability, even in its restricted cognitive sense, which has to do with the agent’s situatedness. On the view I propose, instead, vulnerability is declined as a constitutive constraint on practical reasoning. Susceptibility to time constraints makes sense of the agents’ engagement in action and of their distinctive deliberative perspective. Susceptibility to bodily needs and desires tracks the normative relation between motivations and reasons for action, as well as the corporal roots of the agents’ efficacy in a perceived context. Susceptibility to others makes possible to broaden the scope and the modes of individual agency, by way of inter-action and shared agency. Rather than the source of problems and issues for rational agency, I take vulnerability to name the cluster of constitutive constraints that shape practical reasoning. According to the distinctive variety of Kantian constructivism I defend, practical reason is incomplete, rather than imperfect or defective. The completion of practical reason does not aim to correct or dissolve vulnerability, but deploys vulnerability as a resource to build up autonomy. This view accounts for autonomy as a normative relation among vulnerable agents, which develops in time. (shrink)

The traditional possible-worlds model of belief describes agents as ‘logically omniscient’ in the sense that they believe all logical consequences of what they believe, including all logical truths. This is widely considered a problem if we want to reason about the epistemic lives of non-ideal agents who—much like ordinary human beings—are logically competent, but not logically omniscient. A popular strategy for avoiding logical omniscience centers around the use of impossible worlds: worlds that, in one way or another, violate the laws (...) of logic. In this paper, we argue that existing impossible-worlds models of belief fail to describe agents who are both logically non-omniscient and logically competent. To model such agents, we argue, we need to ‘dynamize’ the impossible-worlds framework in a way that allows us to capture not only what agents believe, but also what they are able to infer from what they believe. In light of this diagnosis, we go on to develop the formal details of a dynamic impossible-worlds framework, and show that it successfully models agents who are both logically non-omniscient and logically competent. (shrink)

In recent years, the human ability to reasoning about mental states of others in order to explain and predict their behavior has come to be a highly active area of research. Researchers from a wide range of fields { from biology and psychology through linguistics to game theory and logic{ contribute new ideas and results. This interdisciplinary workshop, collocated with the Thirteenth International Conference on Theoretical Aspects of Rationality and Knowledge (TARK XIII), aims to shed light on models of (...) social reasoning that take into account realistic resource bounds. People reason about other people's mental states in order to understand and predict the others' behavior. This capability to reason about others' knowledge, beliefs and intentions is often referred to as theory of mind. Idealized rational agents are capable of recursion in their social reasoning, and can reason about phenomena like common knowledge. Such idealized social reasoning has been modeled by modal logics such as epistemic logic and BDI (belief, desire, intention) logics and by epistemic game theory. However, in real-world situations, many people seem to lose track of such recursive social reasoning after only a few levels. The workshop provides a forum for researchers that attempt to analyze, understand and model how resource-bounded agents reason about other minds. (shrink)

We propose a separation logic where resources are histories (sequences) of epistemic actions so that resource update means concatenation of histories and resource decomposition means splitting of histories. This separation logic, called AMHSL, allows us to reason about the past: does what is true now depend on what was true in the past, before certain actions were executed? We show that the multiplicative connectives can be eliminated from a logical language with also epistemic and action model modalities, if (...) the horizon of epistemic actions is bounded. (shrink)

It has long been recognized that the concept of inconsistency is a central part of commonsense reasoning. In this issue, a number of authors have explored the idea of reasoning with maximal consistent subsets of an inconsistent stratified knowledge base. This paradigm, often called “coherent-based reasoning", has resulted in some interesting proposals for para-consistent reasoning, non-monotonic reasoning, and argumentation systems. Unfortunately, coherent-based reasoning is computationally very expensive. This paper harnesses the approach of approximate entailment (...) by Schaerf and Cadoli [SCH 95] to develop the concept of “approximate coherent-based reasoning". To this end, we begin to present a multi-modal propositional logic that incorporates two dual families of modalities: □S and?S defined for each subset S of the set of atomic propositions. The resource parameter S indicates what atoms are taken into account when evaluating formulas. Next, we define resource-bounded consolidation operations that limit and control the generation of maximal consistent subsets of a stratified knowledge base. Then, we present counterparts to existential, universal, and argumentative inference that are prominent in coherence-based approaches. By virtue of modalities □S and?S, these inferences are approximated from below and from above, in an incremental fashion. Based on these features, we show that an anytime view of coherent-based reasoning is tenable. (shrink)

Practical reasoners are resource-bounded—in particular they require time to derive consequences of their knowledge. Building on the Timed Reasoning Logics (TRL) framework introduced in [1], we show how to represent the time required by an agent to reach a given conclusion. TRL allows us to model the kinds of rule application and conflict resolution strategies commonly found in rule-based agents, and we show how the choice of strategy can influence the information an agent can take into account (...) when making decisions at a particular point in time. We prove general completeness and decidability results for TRL, and analyse the impact of communication in an example system consisting of two agents which use different conflict resolution strategies. (shrink)

First, we describe a psychological experiment in which the participants were asked to determine whether sentences of first-order logic were true or false in finite graphs. Second, we define two proof systems for reasoning about truth and falsity in first-order logic. These proof systems feature explicit models of cognitive resources such as declarative memory, procedural memory, working memory, and sensory memory. Third, we describe a computer program that is used to find the smallest proofs in the aforementioned proof systems (...) when capacity limits are put on the cognitive resources. Finally, we investigate the correlation between a number of mathematical complexity measures defined on graphs and sentences and some psychological complexity measures that were recorded in the experiment. (shrink)

“Rationality” in Simon's “bounded rationality” is the principle that humans make decisions on the basis of step-by-step reasoning using systematic rules of logic to maximize utility. “Bounded rationality” is the observation that the ability of a human brain to handle algorithmic complexity and large quantities of data is limited. Bounded rationality, in other words, treats a decision maker as a machine carrying out computations with limited resources. Under the principle of embodied cognition, a cognitive mind is (...) an interactive machine. Turing-Church computations are not interactive, and interactive machines can accomplish things that no Turing-Church computation can accomplish. Hence, if “rationality” is computation, and “bounded rationality” is computation with limited complexity, then “embodied bounded rationality” is both more limited than computation and more powerful. By embracing interaction, embodied bounded rationality can accomplish things that Turing-Church computation alone cannot. Deep neural networks, which have led to a revolution in artificial intelligence, are both interactive and not fundamentally algorithmic. Hence, their ability to mimic some cognitive capabilities far better than prior algorithmic techniques based on symbol manipulation provides empirical evidence for the principle of embodied bounded rationality. (shrink)

Resource Bounded Agents Resource bounded agents are persons who have information processing limitations. All persons and other cognitive agents who have bodies are such that their sensory transducers have limited resolution and discriminatory ability; their information processing speed and power is bounded by some threshold; and their memory and … Continue reading Resource Bounded Agents →.

This paper presents statistical default logic, an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, including hypothesis testing and the estimation of a populations mean, variance and proportions. The logic replaces classical defaults with ordered pairs consisting of a Reiter default in the first coordinate and a real number within the unit interval in the second coordinate. This real number represents an upper-bound limit on the probability of accepting (...) the consequent of an applied default and that consequent being false. A method for constructing extensions is then defined that preserves this upper bound on the probability of error under a (skeptical) non-monotonic consequence relation. (shrink)

In the Newcomb problem, the standard arguments for taking either one box or both boxes adduce what seem to be relevant considerations, but they are not complete arguments, and attempts to complete the arguments rely upon incorrect principles of rational decision making. It is argued that by considering how the predictor is making his prediction, we can generate a more complete argument, and this in turn supports a form of causal decision theory.

A first-order temporal non-commutative logic TN[l], which has no structural rules and has some l-bounded linear-time temporal operators, is introduced as a Gentzen-type sequent calculus. The logic TN[l] allows us to provide not only time-dependent, resource-sensitive, ordered, but also hierarchical reasoning. Decidability, cut-elimination and completeness (w.r.t. phase semantics) theorems are shown for TN[l]. An advantage of TN[l] is its decidability, because the standard first-order linear-time temporal logic is undecidable. A correspondence theorem between TN[l] and a resource (...) indexed non-commutative logic RN[l] is also shown. This theorem is intended to state that “time” is regarded as a “resource”. (shrink)

Syntactic logics do not suffer from the problems of logical omniscience but are often thought to lack interesting properties relating to epistemic notions. By focusing on the case of rule-based agents, I develop a framework for modelling resource-bounded agents and show that the resulting models have a number of interesting properties.

There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein (), charges an agent for doing costly computation; the second, initiated by Neyman (), does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. For the first approach, we take the objects of choice (...) in a decision problem to be Turing machines, and charge players for the “complexity” of the Turing machine chosen (e.g., its running time). This approach can be used to explain well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on) and belief polarization (two people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions) as the outcomes of quite rational decisions. For the second approach, we model people as finite automata, and provide a simple algorithm that, on a problem that captures a number of settings of interest, provably performs optimally as the number of states in the automaton increases. (shrink)

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that (...) are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents. (shrink)

We here describe research into the formal specification and implementation of resource-bounded agents. In particular, we provide an overview of our work on incorporating resource limitations into executable agent specifications. In addition, we outline future directions, highlighting both their promise and their problems.

We propose a framework for modelling situated resource-bounded agents. The framework is based on an objective ascription of intentional modalities and can be easily tailored to the system we want to model and the properties we wish to specify. As an elaboration of the framework, we introduce a logic, OBA, for describing the observations, beliefs, goals and actions of simple agents, and show that OBA is complete, decidable and has an efficient model checking procedure, allowing properties of agents (...) specified in OBA to be verified using standard theorem proving or model checking techniques. (shrink)

Straddling the divide between universalism and relativism, agonistic reason as construed by Foucault and Castoriadis dismisses universal foundations without becoming context-bound or inescapably subjectivist. It is propelled by a strong commitment to freedom and it draws flexibly on available resources and its creative potentials in order to vindicate its conditional claims. This provides a hyper-critical and liberating mode of critical reason which delves into the underlying norms of agency in order to open them up to question and to enhance free (...) self-direction. The argument that is put forward, then, is threefold. Firstly, Castoriadis’ accent on ontological reflection, the imaginative disclosure of new figures and the global intent of critique contrasts with Foucault’s account of agonistic reason and yields a more robust version of critical rationality. Secondly, this form of reflective agonism can effectively address fundamental challenges and reason across contexts, tackling moral and other issues that arise from cultural innovation and exchange. Lastly, agonistic reason need not, and should not, call upon absolute principles on any level in order to uphold its own values and do justice to its radical others. (shrink)

In this paper, we argue that our moral concern for future well-being should reduce over time due to important practical considerations about how humans interact with spacetime. After surveying several of these considerations (around equality, special duties, existential contingency, and overlapping moral concern) we develop a set of core principles that can both explain their moral significance and highlight why this is inherently bound up with our relationship with spacetime. These relate to the equitable distribution of (1) moral concern in (...) a universe that we can only causally affect in one temporal direction; (2) access to the benefits from using spacetime as a resource; and (3) the burdens of care given (1) and (2). We conclude by considering the practical implications of our argument and find that, while it is often assumed that a preference for present over future well-being weakens the case for existential risk mitigation, this likely is not the case. (shrink)

This article presents two theorems: a generalization of Löb’s Theorem that applies to formal proof systems operating with bounded computational resources, such as formal verification software or theorem provers, and a theorem on the robust cooperation of agents that employ proofs about one another’s source code as unexploitable criteria for cooperation. The latter illustrates a capacity for outperforming classical Nash equilibria and correlated equilibria, attaining mutually cooperative program equilibrium in the Prisoner’s Dilemma while remaining unexploitable, i.e., sometimes achieving the (...) outcome, and never receiving the outcome as player 1. (shrink)

The objective of this paper is to construct an implementable theory of rational decision-making for cognitive agents subject to realistic resource constraints. It is argued that decision-making should select actions indirectly by selecting plans that prescribe them. It is also argued that although expected values provide the tool for evaluating plans, plans cannot be compared straightforwardly in terms of their expected values, and the objective of a realistic agent cannot be to find optimal plans. The theory of Locally Global (...) planning is proposed as a realistic alternative to standard "maximizing" theories of rational decision-making. (shrink)

We exhibit a structural difference between the truth-table degrees of the sets which are truth-table above 0′ and the PTIME-Turing degrees of all sets. Though the structures do not have the same isomorphism type, demonstrating this fact relies on developing their common theory.

Epistemic logics based on the possible worlds semantics suffer from the problem of logical omniscience, whereby agents are described as knowing all logical consequences of what they know, including all tautologies. This problem is doubly challenging: on the one hand, agents should be treated as logically non-omniscient, and on the other hand, as moderately logically competent. Many responses to logical omniscience fail to meet this double challenge because the concepts of knowledge and reasoning are not properly separated. In this (...) paper, I present a dynamic logic of knowledge that models an agent’s epistemic state as it evolves over the course of reasoning. I show that the logic does not sacrifice logical competence on the altar of logical non- omniscience. (shrink)

Reductivist programs in logicand philosophy, especially inthe philosophy of mathematics,are reviewed. The paper argues fora ``methodological realism'' towardsnumbers and sets, but still givesreductionism an important place,albeit in methodology/epistemologyrather than in ontology proper.