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)

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a (...) quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience. (shrink)

Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll (...) argue that agents can fail to know trivial consequences of what they know, but never determinately. Such cases are epistemic oversights on behalf of the agent in question, and the facts about epistemic oversights are always indeterminate facts. As a result, we are never in a position to assert that such-and-such constitutes an epistemic oversight for agent i (for we may rationally assert only determinate truths). I then develop formal epistemic models according to which epistemic accessibility relations are vague. Given these models, we can show that epistemic oversights always concern indeterminate cases of knowledge. (shrink)

Rational agents base their actions on information from observation, inference, introspection, or other sources. But this information comes in different kinds, and it is usually handled by different logical mechanisms. We discuss how to integrate external ‘updating information’ and internal ‘elucidating information’ into one system of dynamic epistemic logic, by distinguishing two basic informational actions: ‘bare seeing’ versus ‘conscious realization’.

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)

The logical omniscience problem, whereby standard models of epistemic logic treat an agent as believing all consequences of its beliefs and knowing whatever follows from what else it knows, has received plenty of attention in the literature. But many attempted solutions focus on a fairly narrow specification of the problem: avoiding the closure of belief or knowledge, rather than showing how the proposed logic is of philosophical interest or of use in computer science or artificial intelligence. Sentential epistemic logics, as (...) opposed to traditional possible worlds approaches, do not suffer from the problems of logical omniscience but are often thought to lack interesting epistemic properties. In this paper, I focus on the case of rule-based agents, which play a key role in contemporary AI research but have been neglected in the logical literature. I develop a framework for modelling monotonic, nonmonotonic and introspective rule-based reasoners which have limited cognitive resources and prove that the resulting models have a number of interesting properties. An axiomatization of the resulting logic is given, together with completeness, decidability and complexity results. (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)

Accounts of logical independence which coincide when applied in the case of classical logic diverge elsewhere, raising the question of what a satisfactory all-purpose account of logical independence might look like. ‘All-purpose’ here means: working satisfactorily as applied across different logics, taken as consequence relations. Principal candidate characterizations of independence relative to a consequence relation are that there the consequence relation concerned is determined by only by classes of valuations providing for all possible truth-value combinations for the formulas whose independence (...) is at issue, and that the consequence relation ‘says’ nothing special about how those formulas are related that it does not say about arbitrary formulas. Each of these proposals returns counterintuitive verdicts in certain cases—the truth-value inspired approach classifying certain cases one would like to describe as involving failures of independence as being cases of independence, and the de Jongh approach counting some intuitively independent pairs of formulas as not being independent after all. In final section, a modification of the latter approach is tentatively sketched to correct for these misclassifications. The attention is on conceptual clarification throughout, rather than the provision of technical results. Proofs, as well as further elaborations, are lodged in the ‘longer notes’ in a final Appendix. (shrink)

One of the objectives in the field of artificial intelligence for some decades has been the development of artificial agents capable of coexisting in harmony with people and other systems. The computing research community has made efforts to design artificial agents capable of doing tasks the way people do, tasks requiring cognitive mechanisms such as planning, decision-making, and learning. The application domains of such software agents are evident nowadays. Humans are experiencing the inclusion of artificial agents in their environment as (...) unmanned vehicles, intelligent houses, and humanoid robots capable of caring for people. In this context, research in the field of machine ethics has become more than a hot topic. Machine ethics focuses on developing ethical mechanisms for artificial agents to be capable of engaging in moral behavior. However, there are still crucial challenges in the development of truly Artificial Moral Agents. This paper aims to show the current status of Artificial Moral Agents by analyzing models proposed over the past two decades. As a result of this review, a taxonomy to classify Artificial Moral Agents according to the strategies and criteria used to deal with ethical problems is proposed. The presented review aims to illustrate (1) the complexity of designing and developing ethical mechanisms for this type of agent, and (2) that there is a long way to go (from a technological perspective) before this type of artificial agent can replace human judgment in difficult, surprising or ambiguous moral situations. (shrink)