While logical theories of information attitudes, such as knowledge, certainty and belief, have flourished in the past two decades, formalization of other facets of rational behavior have lagged behind significantly. One intriguing line of research concerns the concept of intention. I will discuss one approach to tackling the notion within a logical framework, based on a database perspective.

There are numerous occasions on which we need to reason about a finite number of events. And we often need to consider only those events which are given or which we perceive. These give rise to the Criteria of Finiteness and Closedness. Allen's logic provides a way of reasoning about events. In this paper I examine Allen and Hayes' axiomatisation of this logic, and develop two other axiomatisations based on the work by Russell and Thomason. I shall show that these (...) three axiomatisations are weakly equivalent, and that only the last two meet the Criteria of Finiteness and Closedness (to different degrees). I shall then examine two ways of constructing instants of time in a finite and closed world, i.e. the Russell construction and the Thomason construction. I shall prove that these two constructions are equivalent under certain conditions. (shrink)

Case-based reasoning has played an important role in legal reasoning systems. As one criteria for similarity of cases, temporal relationsamong affairs in legal cases should be compared. Thus far in many legalreasoning systems, cases have been described as sequences of pointwiseevents, or at best, simple time intervals, and they have been related bypredicates such as before, after, while,and so on. However, such relations may depend on each implementer'spersonal view, and also require much labor to write down by hand. In this (...) paper, we first propose a classification of affair types by their temporal features, and according to those types, we propose several assumption rules that prescribe the temporal relations between affair types. The temporal relations are automatically generated by these rules. Thereafter, we discuss how thesetemporal relations work in the comparison of similarity of cases. Inthe process of comparison, inadequate temporal relations need to beamended. For this purpose, we introduce revision rules, that refute theresults of assumption rules. (shrink)

Most of the descriptions of interval time structures in the first order predicate calculus are based on linear time. However, in the case of intervals, abandoning the condition oflinearity (e.g.LIN in van Benthem's systems) is not sufficient. In this paper, some properties of non-linear time structures are discussed. The most important one is the characterization of location of intervals in a fork of branches. This is connected with the fact that an interval can contain non-collinear subintervals. As a result of (...) non-linearity, some basic properties of interval structures must be formulated in a weaker form. Moreover, time must be filled by intervals to indicate that time cannot pass without events occurring in it. Finally, it is shown that when intervals cannot contain non-collinear subintervals, most of the conditions described in the paper are satisfied. (shrink)

Hybrid languages have both modal and first-order characteristics: a Kripke semantics, and explicit variable binding apparatus. This paper motivates the development of hybrid languages, sketches their history, and examines the expressive power of three hybrid binders. We show that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first-order expressivity can be gained by adding the universal modality, and that all three binders can force the existence of infinite models and have undecidable satisfiability (...) problems. (shrink)

Imagine yourself sitting on your front porch, sipping your morning coffee and admiring the scene before you. You see trees, houses, people, automobiles; you see a cat running across the road, and a bee buzzing among the flowers. You see that the flowers are yellow, and blowing in the wind. You see that the people are moving about, many of them on bicycles. You see that the houses are painted different colors, mostly earth tones, and most are one-story but a (...) few are two-story. It is a beautiful morning. Thus the world interfaces with your mind through your senses. There is a strong intuition that we are not disconnected from the world. We and the other things we see around us are part of a continuous whole, and we have direct access to them through vision, touch, etc. However, the philosophical tradition tries to drive a wedge between us and the world by insisting that the information we get from perception is the result of inference from indirect evidence that is about how things look and feel to us. The philosophical problem of perception is then to explain what justifies these inferences. We will focus on visual perception. Figure one presents a crude diagram of the cognitive system of an agent capable of forming beliefs on the basis of visual perception. Cognition begins with the stimulation of the rods and cones on the retina. From that physical input, some kind of visual processing produces an introspectible visual image. In response to the production of the visual image, the cognizer forms beliefs about his or her surroundings. Some beliefs the perceptual beliefs are formed as direct responses to the visual input, and other beliefs are inferred from the perceptual beliefs. The perceptual beliefs are, at the very least, caused or causally influenced by having the image. This is signified by the dashed arrow marked with a large question mark. We will refer to this as the mystery link. Figure one makes it apparent that in order to fully understand how knowledge is based on perception, we need three different theories.. (shrink)

Tense logic is a branch of contemporary logic which includes formal devices that allow us to deal with the temporal relations between propositions. The aim of our paper is threefold: 1) to reveal how Aristotelian philosophical ideas about time, truth, possibility and necessity were reinterpreted by the founder of contemporay tense logic Arthur Prior; 2) to discuss what novel solutions to the classical problem of future contingents are available using Priorean invention; 3) to describe how the tools of tense logic (...) have transcended their original theoretical purposes. Keywords: Tense Logic, Sea-Battle Paradox, Future Contingents, Arthur Prior, Aristotle. (shrink)

Planlama --- bir amaca ulaşmak üzere bir aksiyonlar bütünü tasarlamak --- yapay zekadaki en temel problemlerden biridir. Bu yazıda, robotikte planlama konusuna mantıkçı (logicist) yaklaşım ele alınmaktadır. [Planning --- devising a plan of action to reach a given goal --- is a fundamental problem in AI. This paper reviews the logicist approach to planning in robotics.].

The Japanese marker _-te-i-_ can have progressive, resultative, and existential perfect readings and has often been regarded as ambiguous. This paper shows that there is no clear evidence that _-te-i-_ is ambiguous. It proposes a monosemous analysis of _-te-i-_ that unifies its multiple readings and shows how progressives and perfects can form a natural semantic class. Within the context of a Discourse Representation Theory, I propose that _-te-i-_ consists of an imperfective operator _-te-_ and a stativizer _-i-_. The imperfective operator (...) _-te-_ takes an eventuality as its argument and outputs a subpart of the eventuality, which precedes a reference time interval. Secondly, a stativizer _-i-_ maps the subpart of the eventuality, i.e. _-te-_'s output, onto a state which overlaps with reference time and whose category is semantically underspecified and is determined via pragmatic inferences. The vague output of the imperfective operator, i.e. whether it is a proper subpart or nonproper subpart of an eventuality, leads to the contrast between progressive readings and perfect readings of _-te-i-_. (shrink)

The question addressed in this paper is how the degree of justification of a belief is determined. A conclusion may be supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. What is sought is a way of computing the “on sum” degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all (...) relevant reasons. (shrink)

Logic has been a—disputed—ingredient in the emergence and development of the now very large field known as knowledge representation and reasoning. In this book (in progress), I select some central topics in this highly fruitful, albeit controversial, association (e.g., non-monotonic reasoning, implicit belief, logical omniscience, closed world assumption), identifying their sources and analyzing/explaining their elaboration in highly influential published work.

The Little Nell Problem was formulated by Drew McDermott in 1982. It reveals unexpected complexities in the interaction of the beliefs and intentions of a planning agent. This paper discusses the problem and proposes a solution.

Artificial agents, which are embedded in a virtual world, need to interpret a sequence of commands given to them adequately, considering the temporal structure for each command. In this paper, we start with the semantics of natural language and classify the temporal structures of various eventualities into such aspectual classes as action, process, and event. In order to formalize these temporal structures, we adopt Arrow Logic. This logic specifies the domain for the valuation of a sentence as an arrow. We (...) can connect, or give order to, arrows by defining inter-arrow operations, and can give different views for sentences. Thereafter we formalize the rules of aspectual shifts in situated inference, in the style of a logic programming language. Thus, we not only describe the static representation of temporal features, but also show the dynamic process to deduce how each eventuality is viewed. The rules are applied to the information flow through the sequence of commands; therefore, we consider how the temporal structure of a command affects the succeeding commands. (shrink)

Intentions are an important concept in Artificial Intelligence and Cognitive Science. We present a formal theory of intentions and beliefs based on Discourse Representation Theory that captures many of their important logical properties. Unlike possible worlds approaches, this theory does not assume that agents are perfect reasoners, and gives a realistic view of their internal architecture; unlike most representational approaches, it has an objective semantics, and does not rely on an ad hoc labeling of the internal states of agents. We (...) describe a minimal logic for intentions and beliefs that is sound and complete relative to our semantics. We discuss several additional axioms, and the constraints on the models that validate them. (shrink)

We identify two pragmatic problems in temporal reasoning, the qualification problem and the extended prediction problem, the latter subsuming the infamous frame problem. Solutions to those seem to call for nonmonotonic inferences, and yet naive use of standard nonmonotonic logics turns out to be inappropriate. Looking for an alternative, we first propose a uniform approach to constructing and understanding nonmonotonic logics. This framework subsumes many existing nonmonotonic formalisms, and yet is remarkably simple, adding almost no extra baggage to traditional logic. (...) We then use this framework to propose a solution to the qualification problem. We also outline a solution to the extended prediction problem, and speculate on a possible connection between the above discussion and the concept of causation. (shrink)

In this paper we show that properties of non-linear time structures have not been studied enough. Axioms forcing the existence of a branching point in a branching area of a structure are presented for various classes of structures. We show also that the classical Dedekind continuity axiom does not work well in non-linear structures and we suggest stronger versions. Finally, some interdependencies between the axioms presented are proved.