The starting point of this paper is earlier work, where we proposed an epistemic logic which characterizes the beliefs of a knowledge-based agent in terms of increasing levels of complexity. At the lowest level, the agent is only able to draw simple conclusions from its knowledge base. Higher levels lead to more and more inferences and computing the beliefs at any particular level turns out to be tractable. What makes this logic arguably appealing is the fact that the underlying semantics is based on possible worlds. However, the work is still limited in that only beliefs about what is true in the world are considered, that is, an agent's beliefs about its own beliefs are ignored. In this paper we will close this gap and generalize the earlier work by proposing a model of limited belief where an agent is able to fully introspect on its own beliefs without sacrificing tractability.

Common sense has always been of interest in AI, but has rarely taken center stage. Despite its mention in one of John McCarthy's earliest papers and years of work by dedicated researchers, arguably no AI system with a serious amount of general common sense has ever emerged. Why is that? What's missing? Examples of AI systems' failures of common sense abound, and they point to AI's frequent focus on expertise as the cause. Those attempting to break the brittleness barrier, even in the context of modern deep learning, have tended to invest their energy in large numbers of small bits of commonsense knowledge. But all the commonsense knowledge fragments in the world don't add up to a system that actually demonstrates common sense in a human-like way. We advocate examining common sense from a broader perspective than in the past. Common sense is more complex than it has been taken to be and is worthy of its own scientific exploration.

Agents change their beliefs about the plausibility of various aspects of domain dynamics -- effects of physical actions, results of sensing, and action preconditions -- as a consequence of their interactions with the world. In this paper we propose a way to conveniently represent domain dynamics in the situation calculus to support such belief change. Furthermore, we suggest patterns to follow when writing the axioms that describe the effects of actions, and prove how these patterns can control the extent to which observations change the agent's beliefs about action effects. We also discuss the relation of our work to the AGM postulates for belief revision. Finally, we show how beliefs about domain dynamics can be incorporated into a form of regression rewriting to support reasoning.

In a recent paper Lakemeyer and Levesque proposed a first-order logic of limited belief to characterize the beliefs of a knowledge base (\KB). Among other things, they show that their model of belief is expressive, eventually complete, and tractable. This means, roughly, that a \KB\ may consist of arbitrary first-order sentences, that any sentence which is logically entailed by the \KB\ is eventually believed, given enough reasoning effort, and that reasoning is tractable under reasonable assumptions. One downside of the proposal is that epistemic states are defined in terms of sets of clauses, possibly containing variables, giving the logic a distinct syntactic flavour compared to the more traditional possible-world semantics found in the literature on epistemic logic. In this paper we show that the same properties as above can be obtained by defining epistemic states as sets of three-valued possible worlds. This way we are able to shed new light on those properties by recasting them using the more familiar notion of truth over possible worlds.

In knowledge representation, obtaining a notion of belief which is tractable, expressive, and eventually complete has been a somewhat elusive goal. Expressivity here means that an agent should be able to hold arbitrary beliefs in a very expressive language like that of first-order logic, but without being required to perform full logical reasoning on those beliefs. Eventual completeness means that any logical consequence of what is believed will eventually come to be believed, given enough reasoning effort. Tractability in a first-order setting has been a research topic for many years, but in most cases limitations were needed on the form of what was believed, and eventual completeness was so far restricted to the propositional case. In this paper, we propose a novel logic of limited belief, which has all three desired properties.

Only knowing captures the intuitive notion that the beliefs of an agent are precisely those that follow from its knowledge base. It has previously been shown to be useful in characterizing knowledge-based reasoners, especially in a quantified setting. While this allows us to reason about incomplete knowledge in the sense of not knowing whether a formula is true or not, there are many applications where one would like to reason about the degree of belief in a formula. In this work, we propose a new general first-order account of probability and only knowing that admits knowledge bases with incomplete and probabilistic specifications. Beliefs and non-beliefs are then shown to emerge as a direct logical consequence of the sentences of the knowledge base at a corresponding level of specificity.

The area of cognitive robotics is often subject to the criticism that the proposals investigated in the literature are too far removed from the kind of continuous uncertainty and noise seen in actual real-world robotics. This paper proposes a new language and an implemented system, called PREGO, based on the situation calculus, that is able to reason effectively about degrees of belief against noisy sensors and effectors in continuous domains. It embodies the representational richness of conventional logic-based action languages, such as context-sensitive successor state axioms, but is still shown to be efficient using a number of empirical evaluations. We believe that PREGO is a powerful framework for exploring real-time reactivity and an interesting bridge between logic and probability for cognitive robotics applications.

This work develops an approach to efficient reasoning in first-order knowledge bases with incomplete information. We build on Levesque's proper knowledge bases approach, which supports limited incomplete knowledge in the form of a possibly infinite set of positive or negative ground facts. We propose a generalization which allows these facts to involve unknown individuals, as in the work on labeled null values in databases. Dealing with such unknown individuals has been shown to be a key feature in the database literature on data integration and data exchange. In this way, we obtain one of the most expressive first-order open-world settings for which reasoning can still be done efficiently by evaluation, as in relational databases. We show the soundness of the reasoning procedure and its completeness for queries in a certain normal form.

A plan with rich control structures like branches and loops can usually serve as a general solution that solves multiple planning instances in a domain. However, the correctness of such generalized plans is non-trivial to define and verify, especially when it comes to whether or not a plan works for all of the infinitely many instances of the problem. In this paper, we give a precise definition of a generalized plan representation called an FSA plan, with its semantics defined in the situation calculus. Based on this, we identify a class of infinite planning problems, which we call one-dimensional (1d), and prove a correctness result that 1d problems can be verified by finite means. We show that this theoretical result leads to an algorithm that does this verification practically, and a planner based on this verification algorithm efficiently generates provably correct plans for 1d problems.

Although there has been much discussion of belief change (e.g. [4, 21]), goal change has not received much attention. In this paper, we propose a method for goal change in the framework of Reiter's; [12] theory of action in the situation calculus [8, 10], and investigate its properties. We extend the framework developed by Shapiro et al. [17] and Shapiro and Lespérance [16], where goals and goal expansion were modelled, but goal contraction was not.

When it comes to building controllers for robots or agents, high level programming languages like Golog and ConGolog offer a useful compromise between planning-based approaches and low-level robot programming. However, two serious problems typically emerge in practical implementations of these languages: how to evaluate test in a program efficiently enough in an open-world setting, and how to make appropiate nondeterministic choices while avoiding full lookahead. Recent proposals in the literature suggest that one could tackle the first problem by exploiting sensing information, and tackle the second by specifying the amount of lookahead allowed explicitly in the program. In this paper, we combine these two ideas and demonstrate their power by presenting an interpreter, written in Prolog, for a variant of Golog that is suitable for efficiently operating in open-world setting by exploiting sensing and bounded lookahead.

A crucially important adequacy test of any theory of speech acts is its ability to handle performatives. This paper provides a theory of performatives as a test case for our rationally based theory of illocutionary acts. We show why "I request you..." is a request, and "I lie to you that p" is self-defeating. The analysis supports and extends earlier work of theorists such as Bach and Harnish [1] and takes issue with recent claims by Searle [10] that such performative-as-declarative analyses are doomed to failure.

The relative expressive power of a sentential operator □α is compared to that of a syntactical predicateL(‘α’) in the setting of first‐order logics. Despite well‐known results by Montague and by Thomason that claim otherwise, any of the so‐called “modal” logics of knowledge and belief can be compiled into classical first‐order logics that have a corresponding predicate on sentences. Moreover, through the use of a partial truth predicate, the standard modal axiom schemata can be translated into single sentences, making it possible to use conventional first‐order logic theorem provers to directly derive results in a wide class of modal logics.

A fundamental computational limit on automated reasoning and its effect on knowledge representation is examined. Basically, the problem is that it can be more difficult to reason correctly with one representational language than with another and, moreover, that this difficulty increases dramatically as the expressive power of the language increases. This leads to a tradeoff between the expressiveness of a representational language and its computational tractability. Here we show that this tradeoff can be seen to underlie the differences among a number of existing representational formalisms, in addition to motivating many of the current research issues in knowledge representation.

This paper derives the basis of a theory of communication from a formal theory of rational interaction. The major result is a demonstration that illocutionary acts need not be primitive, and need not be recognized. As a test case. we derive Searle's conditions on requesting from principles of rationality coupled with a Gricean theory of imperatives. The theory is shown to distinguish insincere or nonserious imperatives from true requests. Extensions to indirect speech acts, and ramifications for natural language systems are also briefly discussed.