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)

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)

Although the change of beliefs in the face of new information has been widely studied with some success, the revision of other mental states has received little attention from the theoretical perspective. In particular, intentions are widely recognised as being a key attitude for rational agents, and while several formal theories of intention have been proposed in the literature, the logic of intention revision has been hardly considered. There are several reasons for this: perhaps most importantly, intentions are very closely (...) connected with other mental states—in particular, beliefs about the future and the abilities of the agent. So, we cannot study them in isolation. We must consider the interplay between intention revision and the revision of other mental states, which complicates the picture considerably. In this paper, we present some first steps towards a theory of intention revision. We develop a simple model of an agent’s mental states, and define intention revision operators. Using this model, we develop a logic of intention dynamics, and then investigate some of its properties. (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)

Default reasoning occurs whenever the truth of the evidence available to the reasoner does not guarantee the truth of the conclusion being drawn. Despite this, one is entitled to draw the conclusion “by default” on the grounds that we have no information which would make us doubt that the inference should be drawn. It is the type of conclusion we draw in the ordinary world and ordinary situations in which we find ourselves. Formally speaking, ‘nonmonotonic reasoning’ refers to argumentation in (...) which one uses certain information to reach a conclusion, but where it is possible that adding some further information to those very same premises could make one want to retract the original conclusion. It is easily seen that the informal notion of default reasoning manifests a type of nonmonotonic reasoning. Generally speaking, default statements are said to be true about the class of objects they describe, despite the acknowledged existence of “exceptional instances” of the class. In the absence of explicit information that an object is one of the exceptions we are enjoined to apply the default statement to the object. But further information may later tell us that the object is in fact one of the exceptions. So this is one of the points where nonmonotonicity resides in default reasoning. (shrink)

It is suggested that taking into account considerations that traditionally fall within the scope of computer science in general, and artificial intelligence in particular, sheds new light on the subject of causation. It is argued that adopting causal notions con be viewed as filling a computational need: They allow reasoning with incomplete information, facilitate economical representations, and afford relatively efficient methods for reasoning about those representations. Specifically, it is proposed that causal reasoning is intimately bound to nonmonotonic reasoning. An account (...) of causation is offered that relies upon this connection, and compares this proposal to previous accounts within philosophy and artificial intelligence. (shrink)

This work aims to make tense logic a more robust tool for ontologists, philosophers, knowledge engineers and programmers by outlining a fusion of tense logic and ontology of time. In order to make tense logic better understandable, the central formal primitives of standard tense logic are derived as theorems from an informal and intuitive ontology of time. In order to make formulation of temporal propositions easier, temporal operators that were introduced by Georg Henrik von Wright are developed, and mapped to (...) the ontology of time. (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)

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.

So-called ‘reified temporal logics’ were introduced by researchers in Artificial Intelligence (AI) in the early 1980s, and gave rise to a long-running series of debates concerning the proper way to represent states, events, causation, action, and other notions identified as crucial to the knowledge representation needs of AI. These debates never resulted in a definitive resolution of the issues under discussion, and indeed continue to produce aftershocks to the present day; none the less, we are now sufficiently far removed in (...) time from their heyday for it to be a worthwhile exercise to stand back and review them as a connected piece of history. (shrink)

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)

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.].

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. (shrink)

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)

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)