Two-Dimensional Awareness Logics

Awareness logic is a type of belief logic in which an agent's beliefs are restricted to those sentences that the agent is aware of. Awareness logic is a successful way to circumvent the problem of omniscience so that actual belief is modelled in a reasonable way. In this paper, we suggest a new method modelling awareness and actual belief by using two-dimensional logics. We show that the two-dimensional logics are flexible tools. Different types of concepts of awareness can be easily modelled by this method.     

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.     

Is Modernism Really Modern? Uncovering a Fallacy in Postmodernism

Some postmodernists criticize the view that the logics of Western thought can be employed universally. In doing so, they assume without adequate proof that different human societies have greatly different rationalities and employ completely different logics. This essay argues that, on the contrary, widely different cultures often share noteworthy similarities in rationality.     

Using temporal logics of knowledge for specification and verification—a case study

Temporal logics of knowledge are useful for reasoning about situations where the knowledge of an agent or component is important, and where change in this knowledge may occur over time. Here we use temporal logics of knowledge to reason about the game Cluedo. We show how to specify Cluedo using temporal logics of knowledge and prove statements about the knowledge of the players using a clausal resolution calculus for this logic. We discuss the advantages and disadvantages of using this logic to specify and verify the game Cluedo and describe related implementations.     

A verification framework for agent programming with declarative goals

A long and lasting problem in agent research has been to close the gap between agent logics and agent programming frameworks. The main reason for this problem of establishing a link between agent logics and agent programming frameworks is identified and explained by the fact that agent programming frameworks have hardly incorporated the concept of a declarative goal. Instead, such frameworks have focused mainly on plans or goals-to-do instead of the end goals to be realised which are also called goals-to-be. In this paper, the programming language GOAL is introduced which incorporates such declarative goals. The notion of a commitment strategy—one of the main theoretical insights due to agent logics, which explains the relation between beliefs and goals—is used to construct a computational semantics for GOAL. Finally, a proof theory for proving properties of GOAL agents is introduced. Thus, the main contribution of this paper, rather than the language GOAL itself, is that we offer a complete theory of agent programming in the sense that our theory provides both for a programming framework and a programming logic for such agents. An example program is proven correct by using this programming logic.     

Why Combine Logics?

Combining logics has become a rapidly expanding entreprise that is inspired mainly by concerns about modularity and the wish to join together tailor made logical tools into more powerful but still manageable ones. A natural question is whether it offers anything new over and above existing standard languages.By analysing a number of applications where combined logics arise, we argue that combined logics are a potentially valuable tool in applied logic, and that endorsements of standard languages often miss the point. Using the history of quantified modal logic as our main example, we also show that the use of combined structures and logics is a recurring theme in the analysis of existing logical systems.     

Transfers between Logics and their Applications

In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, syntactical structure, and internal transformations. In particular, we treat Belief Revision Systems (BRS) as our main example, defining the Wide Belief Revision Systems (WBRS's). This generalization allows us to define BRS's in an abstract setting for classical and non-standard logics. We also show how the concept of translation between logics can be obtained as a particular case of transfers.     

The Modal Logic of Bayesian Belief Revision

In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable.

     

Shortcuts and Dynamic Marking in the Tableau Method for Adaptive Logics

Adaptive logics typically pertain to reasoning procedures for which there is no positive test. In [7], we presented a tableau method for two inconsistency-adaptive logics. In the present paper, we describe these methods and present several ways to increase their efficiency. This culminates in a dynamic marking procedure that indicates which branches have to be extended first, and thus guides one towards a decision — the conclusion follows or does not follow — in a very economical way.     

Adaptive Logic as a Modal Logic

Modal logics have in the past been used as a unifying framework for the minimality semantics used in defeasible inference, conditional logic, and belief revision. The main aim of the present paper is to add adaptive logics, a general framework for a wide range of defeasible reasoning forms developed by Diderik Batens and his co-workers, to the growing list of formalisms that can be studied with the tools and methods of contemporary modal logic. By characterising the class of abnormality models, this aim is achieved at the level of the model-theory. By proposing formulae that express the consequence relation of adaptive logic in the object-language, the same aim is also partially achieved at the syntactical level.     

Behavioral Algebraization of Logics

We introduce and study a new approach to the theory of abstract algebraic logic (AAL) that explores the use of many-sorted behavioral logic in the role traditionally played by unsorted equational logic. Our aim is to extend the range of applicability of AAL toward providing a meaningful algebraic counterpart also to logics with a many-sorted language, and possibly including non-truth-functional connectives. The proposed behavioral approach covers logics which are not algebraizable according to the standard approach, while also bringing a new algebraic perspective to logics which are algebraizable using the standard tools of AAL. Furthermore, we pave the way toward a robust behavioral theory of AAL, namely by providing a behavioral version of the Leibniz operator which allows us to generalize the traditional Leibniz hierarchy, as well as several well-known characterization results. A number of meaningful examples will be used to illustrate the novelties and advantages of the approach. Presented by Daniele Mundici     

Theism and Dialetheism

The divine attributes of omniscience and omnipotence have faced objections to their very consistency. Such objections rely on reasoning parallel to semantic paradoxes such as the Liar or to set-theoretic paradoxes like Russell's paradox. With the advent of paraconsistent logics, dialetheism—the view that some contradictions are true—became a major player in the search for a solution to such paradoxes. This paper explores whether dialetheism, armed with the tools of paraconsistent logics, has the resources to respond to the objections levelled against the divine attributes.     

Process and Action: Relevant Theory and Logics

Whileprocess andaction are fundamental notions, in ubiquitous use, they lack satisfactory logical treatment in two critical respects: in analyses of the fundamentals themselves and in logical development. For what treatment they have so far received, under classical systematisation, leaves significant lacunae and induces much paradox. A relevant logical relocation, carried through in detail here, removes such problems, and provides solid ground-work for a satisfactory treatment.Firstly, as to fundamentals: processes should be explicated, so it is argued, as certain sorts of (time) directed functions (from inputs to outputs); thus they can be represented through certain ordered pairs of relations. Significant logical structures they can enter into are investigated: notably, process lattice and coupled logics, and a generalized category theory (tolerating nonassociativity of composition).Actions are types of processes, agent-ascribed process. As stock analyses of the differentia, operators and agency, through intentionality, rationality and so on, demonstrably fail, new causal analyses are proposed.Secondly, as to logical developments: for the most part, the apparently diverse offering of process and action logics to be encountered in the literature are but multiple modal logics: modal logics enriched with further functors of interesting modal sorts. Some, for example, like advertised process logics are dynamic logics (themselves basically multiple modal logics) enriched by tense logical functors, themselves modal in character. In a way that is now becoming nonstandardly standard, these modal enterprises can be reworked on relevant logical bases. A main point to such exercises resembles that of other relevant reworkings: namely, the search for correctness, for adequacy to pre-analytic and linguistic data, and therewith removal of paradoxes and anomalies that accumulate under modal analyses.Logical components from a properly expanded Humean model of action are supplied with relevant logics and semantics, in particulardoing, trying andstriving, intention andmotivation. The difficult question of formalising practical inference is then addressed.Relevant dynamic logics, paralleling modal developments, are built up piece by piece, relevant theory change is considered within a dynamic framework, and work on relevant temporal and process logics of programming cast, including functors such asbefore, during andthroughout, is initiated. The present state of logical play is assessed.I have been much encouraged in this work by Krister Segerberg, who deserves and has my considerable thanks. It will be evident that his fine investigative work, which I want to seefurthered, has served as a foil in much of what follows.     

Some Embedding Theorems for Conditional Logic

We prove some embedding theorems for classical conditional logic, covering ‘finitely cumulative’ logics, ‘preferential’ logics and what we call ‘semi-monotonic’ logics. Technical tools called ‘partial frames’ and ‘frame morphisms’ in the context of neighborhood semantics are used in the proof.     

一类命题逻辑的一般弱框架择类语义

命题逻辑的一般弱框架择类语义是相干邻域语义的变形,其特点是：采用择类运算来刻画逻辑常项;语义运算与逻辑联结词之间有清晰的对应关系,可以从整体上处理一类逻辑,具有普适性。本文将这种语义用于一类B、C、K、W命题逻辑,包括相干逻辑R及其线性片段、直觉主义逻辑及其BCK片段等,并借助典范框架和典范赋值,证明了这些逻辑系统的可靠性和完全性。     

Every Finitely Reducible Logic has the Finite Model Property with Respect to the Class of ♦-Formulae

In this paper a unified framework for dealing with a broad family of propositional multimodal logics is developed. The key tools for presentation of the logics are the notions of closure relation operation and monotonous relation operation. The two classes of logics: FiRe-logics (finitely reducible logics) and LaFiRe-logics (FiRe-logics with local agreement of accessibility relations) are introduced within the proposed framework. Further classes of logics can be handled indirectly by means of suitable translations. It is shown that the logics from these classes have the finite model property with respect to the class of -formulae, i.e. each -formula has a -model iff it has a finite -model. Roughly speaking, a -formula is logically equivalent to a formula in negative normal form without occurrences of modal operators with necessity force. In the proof we introduce a substantial modification of Claudio Cerrato's filtration technique that has been originally designed for graded modal logics. The main core of the proof consists in building adequate restrictions of models while preserving the semantics of the operators used to build terms indexing the modal operators.     

On the Poverty of Scientism, or: The Ineluctable Roughness of Rationality

If there is one rationality there must be a plurality of them. This conclusion follows, I argue, partly from the extreme and ineradicable vagueness of the fundamental concepts that every would-be rational explanation must presuppose. Logicistic/scientistic assaults on this vagueness are doomed to fail partly because they are unable to acknowledge the imaginative dimension of rational thought. Being limited to the play of "outward appearances," scientific investigations are also dependent on "inward imaginings" on their speculative side. The upshot is that schools of philosophy should be characterized by the kind of imaginary they adopt rather than by their logics. In which case, every attempt to get and tell something right about the world is bound to incorporate mythopoeic elements in its explanations.     

An analytic tableau calculus for a temporalised belief logic

A tableau is a refutation-based decision procedure for a related logic, and is among the most popular proof procedures for modal logics. In this paper, we present a labelled tableau calculus for a temporalised belief logic called TML⁺, which is obtained by adding a linear-time temporal logic onto a belief logic by the temporalisation method of Finger and Gabbay. We first establish the soundness and the completeness of the labelled tableau calculus based on the soundness and completeness results of its constituent logics. We then sketch a resolution-type proof procedure that complements the tableau calculus and also propose a model checking algorithm for TML⁺ based on the recent results for model checking procedures for temporalised logics. TML⁺ is suitable for formalising trust and agent beliefs and reasoning about their evolution for agent-based systems. Based on the logic TML⁺, the proposed labelled tableau calculus could be used for analysis, design and verification of agent-based systems operating in dynamic environments.     

Self Torture and Group Beneficence

Moral puzzles about actions which bring about very small or what are said to be imperceptible harms or benefits for each of a large number of people are well known. Less well known is an argument by Warren Quinn that standard theories of rationality can lead an agent to end up torturing himself or herself in a completely foreseeable way, and that this shows that standard theories of rationality need to be revised. We show where Quinn's argument goes wrong, and apply this to the moral puzzles.