Conditional Logic

So this is the first chapter which will later the formal groundwork of what I want to do, weak preference as the deontic accessibility. So this is the outline of today: first session, accessibility of modality, and then the modal theory of ethics, a utility theory of weak preference, and a weak preference theory of deontic accessibility. You see what they are. So this is the first section. When we talk about logic, we always the usual approach is that when we use a Aristotelian sentential logic, there's something that we can't say, right? Let's say John has a wife, Mary is Peter's wife, and therefore Peter has a wife. That's something that sentential logic, traditional sentential logic, can't do, and then that therefore we need predicate logic. We need subject-predicate terms, and we also need quantifiers, existential and universal. That's usually the motivation. And then even with quantifier logic or quantification logic, we still cannot represent the sentence up above: "Adolf Hitler could have won and thus peace is not guaranteed." Because now we have modality, and only quantification logic doesn't seem to capture the sentence. And if we were to lay out the sentences that come to the conclusion, it is as if... so if we try to squeeze in a predicate that's "could have been" predicate, it might work or it might not. But at least now we have a modal logic. If, given some other auxiliary premises, given that it's possible that Adolf Hitler could have won... it's possible that Adolf Hitler win... and then given some other premises, we can conclude that peace is not necessary. So with the modal logic, the modal operators, we can do a little bit more. So that's modality. And this is all syntactic or sentential, or how we do proofs, right? But then there comes a possible world semantics, or the possible world theory of modality, that interprets "possibly P" as there are possible worlds in which P, and "necessarily P" as all possible worlds are those in which P. I'll ignore some complicated issues with "necessarily that I'm fat and not fat" because in all possible worlds I am fat and not fat-there are no possible worlds in which I'm that-and I ignore that issue here.

An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantum computation.

Abstract:-Reasoning about real-world problems is only possible if assumptions are made. Assumptions can be formulated as constraints or requirements that must be satisfied. The aim of introducing assumption, whether implicit or explicit, is usually to circumscribe the domain and/or to restrict the complexity of the problem. In this paper, we present a three-valued nonmonotonic logic system L3 that is naturally suitable for diagnostic reasoning and allows us to represent and reason about assumptions employed in approaches to ...

This paper compares two logical conditionals which are strengthenings of the strict conditional and avoid the paradoxes of strict implication. The logics of both may be viewed as extensions of KT, and the two conditionals are interdefinable in KT. The implicative conditional requires that its antecedent and consequent be both contingent. The consequential conditional may be viewed as a weakening of the implicative conditional, insofar as it also admits the case in which the antecedent and the consequent are strictly equivalent (either both necessary or both impossible). The two conditionals share a number of properties, among them Transitivity, Contraposition, Aristotle's Thesis, Weak Boethius' Thesis and Aristotle's Second Thesis. They also share some restricted principles such as Possibilistic Monotonicity, Possibilistic Simplification and Possibilistic Right Weakening. They differ in relation to Identity, which is validated by consequential implication, while the implicative conditional only validates the restricted principle of Possibilistic Identity. The relations between the two conditionals are represented by two Aristotelian cubes of opposition, one involving the contrariety between If A, then B and If A, then ¬B, according to Weak Boethius' Thesis, and the other the contrariety between If A, then B and If ¬A, then B, according to Aristotle's Second Thesis. We also explore the relations between the two logical conditionals and natural language conditionals, emphasizing the dependence of the latter on the context, and the need to distinguish natural language conditionals which may be viewed as consequential or implicative, on one side, and concessive and some other types of conditionals, on the other.

Abstract. In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the possible world semantics for conditional logics. The label formalism introduced in [AG94,ABGR96] to account for the semantics of normal modal logics is easily adapted to the semantics of conditional logics by simply indexing labels with formulas. The inference rules are provided by the propositional system KE + — a tableau-like analytic proof system devised to be used both as a refutation and a direct method of proof — enlarged with suitable elimination rules for the conditional connective. The theorem proving methodology we are going to present can be viewed as a first step towards developing an appropriate algorithmic framework for several conditional logics for (defeasible) conditional obligation.

During his philosophical career Popper sought to characterize natural laws alternately as strictly universal and as 'naturally' or 'physically' necessary statements. In this paper we argue that neither characterization does what Popper claimed and sketch a reconstruction of his views that avoids some of their major drawbacks.

In this paper, we describe a Prolog implementation of a new theorem prover for (normal propositional) modal and multi-modal logics. The theorem prover, which is called KEM , arises from the combination of a classical refutation system which incorporates a restricted ("analytic") version of the cut rule with a label formalism which allows for a specialised, logic-dependent unification algorithm. An essential feature of KEM is that it yields a rather simple and efficient proof search procedure which offers many computational advantages over the usual tableau-based proof search methods. This is due partly to the use of linear 2-premise β rules in place of the branching β rules of the standard tableau method, and partly to the crucial role played by the analytic cut (the only branching rule) in eliminating redundancy from the search space. It turns out that KEM method of proof search is not only computationally more efficient but also intuitively more natural than other (e.g. resolution-based) methods leading to simple and easily implementable procedures (two KEM Theorem Prover-like systems have been implemented: an LPA interpreter on Macintosh, and a Quintus compiler on Sun-Sparcstation) which make it well suited for efficient automated proof search in modal logics. 1 An overview of KEM KEM [AG94, Gov95] is a tableau-like modal proof system based on D'Agostino and Mondadori's [DM94] classical refutation system KE. The basic feature of KEM is that it uses KE rules in combination with a label unification scheme constituted of (1) a label formalism, and (2) a specialised, logic-dependent unification algorithm. The label formalism arises from two (non empty) sets Φ C =

The tableau-like proof system KEM has been proven to be able to cope with a wide variety of (normal) modal logics. KEM is based on D'Agostino and Mondadori's (1994) classical proof system KE, a combination of tableau and natural deduction inference rules which allows for a ...

In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the propositional system KE + -a tableau-like analytic proof system devised to be used both as a refutation method and a direct method of proof-that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.

No contributions by others. No works submitted towards another degree have been included in this thesis. No animal or human subjects were involved in this research. I would like to thank my supervisors. First and foremost, I would like to express sincere gratitude to my supervisor Dominic Hyde for his invaluable critical input and intellectual inspiration, boundless patience, encouragement and guidance. Without his wholehearted and unfailing support over the years, which by far surpassed any formal responsibilities or expectations, this thesis would not have been completed. I am grateful to my supervisor Toby Meadows for his meticulous and insightful critical input in ensuring that key parts of the thesis meet the highest of standards. The thesis has improved immensely as a direct consequence of working with him. I would also like to thank Joel Katzav for his diligent reading of the entire thesis draft, valuable feedback during the final stages of the writing process, and guidance in ensuring that the thesis is completed on time. I would also like to thank the examination committee -Franz Berto and Ed Maresfor their valuable critical remarks and advice regarding publication of the dissertation's content. This research was supported by Australian Postgraduate Award Scholarship.

Although modal logic has significantly developed since the possible worlds semantics invention, today, it is recognized that a modal logic that uses only one type of modality is very restricted. In this article, I aim to provide the semantics and tableaux systems for some alethic-epistemic-doxastic logics. The basic system (T/T/KD*) is used to discuss the validity of some principles and some of Spinoza's ideas on modal thinking, for he believed that the possibility and contingency ideas are defects of our cognition. Next, the system's extensions based on are used to discuss the validity of the doxastic, epistemic, and alethic closure principles by means of the distinction between absolute and relative knowledge. Finally, the system is extended to develop a pair of conditional epistemic-doxastic logics to evaluate some skeptical statements.

The model-based diagnostic approach was first introduced to overcome the limitations of heuristic systems. However, research on model-based systems showed that the model-based diagnosis approaches resort to assumptions that can be viewed as the return, though controlled, of heuristics into diagnostic reasoning. In this paper we focus on diagnosis with component-oriented device models. We argue for the need to represent and reason with these assumptions. We present a conditional logic, DL, That is suitable for diagnostic reasoning and allows us to represent and reason with assumptions.

In Stalnaker's notation, the principle of conditional excluded middle is written as (A>C)⋁(A>¬C) (Stalnaker 1980: 89). David Lewis claims that Stalnaker's theory of counterfactual involves two assumptions: uniqueness assumption and limit assumption. To accept uniqueness assumption is to accept the validity of the principle of conditional excluded middle. Lewis contends that Stalnaker's two assumptions cannot grasp comparative similarities between possible worlds. Stalnaker responds that his theory with supervaluation can avoid the problems. This paper shows that how can supervaluation resolve semantic indeterminacy and save the principle of conditional excluded middle.

The dispute about positivism in German sociology dealt basically with the question, whether we can know what we ought to do or whether we must be content to decide what we want to do. Habermas questioned the distinction which "positivists" and "decisionists" draw between science on the one hand and ethics on the other. Later he proposed his own notion of knowledge about reality and along with it a notion of normative or ethical knowledge and he claimed the two notions were comparable. He developed the first notion in the form of a consensus theory of the truth of statements and the second one in the form of a consensus theory of the righmess of norms and values. The consensus theories are examined and it is shown that both are untenable for various reasons. t. Wenn wir uns an die Sprachregelung halten, nach der nut sicheres Wissen Erkenntnis genannt wird, dann gibt es Erkennmis nur in den Formalwissenschaften und wir miissen dann sagen, Habermas behaupte, wir k6nnten in dem gleichen Sinne wissen was wir tun soUen, in dem wir auch wissen, was ist. Diese Behauptung wotlen wir priifen, denn Habermas postutiert offenbar nur, wir k6nnten eine richtige Meinung hinsichtlich dessen haben, was wir tun sollen, und eine wahre Meinung hinsichtlich dessen, was ist, und die Richtigkeit sei mit der Wahrheit vergleichbar. Abet er postuliert nicht auch, wit k6nnten uns der Wahrheit oder der Richtigkeit unserer Meinungen sicher sein. Deshalb brauchen wir f~ir unsere Zwecke die Frage, ob wir etwas erkennen k6nnen, nicht mehr von der Frage zu unterscheiden, ob wires wissen k6nnen. Wenn es noch einen Unterschied in der Bedeutung gibt, dann meint ,,erkennen" den Vorgang an dessen Ende das Resultat ,,wissen" steht. Der Positivismusstreit begann im Oktober 1961. Auf der Ttibinger Arbeitstagung der Deutschen Gesellschaft f/Jr Soziologie hielten Adorno und Popper Referate. Adorno vertrat die Meinung, es sei m6glich zu erkennen, was wir tun sollen. ~Popper bestritt das. Sp~iter griffen Habermas und Albert das Thema auf und diskutierten es in einer Reihe yon Aufs~itzen. Habermas waft seinen Opponenten, den kritischen Rationatisten, vor, sie reduzierten Erkennmis positivistisch auf Erfahrungswissenschaft 1. Mit diesem Vorwurf trifft er natiirlich auch andere Philosophen. Die Frage, welche Ziele wir verfolgen sollen und welche Zwecke wir uns setzten solten, hielten sie fiir wissenschaft-24* i Habermas (1963), p. 175.

This is the annual report for the Hydrogen Storage Engineering Center of Excellence project as required by DOE EERE's Fuel Cell Technologies Office. We have been provided with a specific format. It describes the work that was done with cryo-sorbent based and chemical-based hydrogen storage materials. Balance of plant components were developed, proof-of-concept testing performed, system costs estimated, and transient models validated as part of this work.

Abstract An operator ⇤! is said to be Boethian in a logic L iff it is either primitive or
defined inLand (i)Lcontains the so-called Boethius’ Thesis ! ⇤! ⌫ # ¬(! ⇤! ¬⌫); (ii) the wffs (! # ⌫) # ! ⇤! ⌫ and ! ⇤! ⌫ # ⌫ ⇤! ! are not L-theorems. The aim of the paper is to show how a Boethian operator may be generated by suitable definitions from non-Boethian operators such as strict implication (J) and Stalnaker-  Lewis conditional (>). The schemata of the two proposed definitions are ! ⌫ =df ! J ⌫ & X and ! +! ⌫ =df ! > ⌫ & X where X is a wff in the two sets A￿￿ = {!, ¬!,⇤!,⇤¬!, ⌃!, ⌃¬!} or C￿￿￿ = {⌫, ¬⌫,⇤⌫,⇤¬⌫, ⌃⌫, ⌃¬⌫}. It is proved that, if the background system for strict implication is the modal system KD, the only modal instance of X which grants the properties of a Boethian operator is the wff ⌃!. A drawback of this definition of is that it does not allows proving Identity, i.e. ! !. In order to justify Identity a more refined analysis requires that the values of X be chosen not only in A￿￿ and C￿￿￿ but also in the set of disjunctive wffs {⌫ _ ⌃!, ¬⌫ _ ⌃!, ⌃⌫ _ ⌃!, ⌃¬⌫ _ ⌃!,⇤¬⌫ _ ⌃!,⇤⌫ _ ⌃!}. It turns out that
in this set the only two values of X which yield Boethian operators are ⇤¬⌫ _ ⌃! and ⇤⌫ _ ⌃!. The former turns out to be equivalent to a consequential operator axiomatized in Pizzi [7], the latter is equivalent to another one which has been axiomatized in Lowe [4]. It is proved in section 4.6 that the former is the only value of X that grants Identity. In the second part of the paper the same schema of analysis is applied to Lewis’ conditional operator >, while the background system is the conditional system VW−. It turns out that the modal values of X in A￿￿ and C￿￿￿
which allow defining a Boethian operator +! are not only ⌃! but also ⇤! and ⇤⌫. Given that all them fail to grant Identity, the values of X must again be chosen in a set of disjunctive statements, which however is wider than the one for . For both and +! an investigation is performed in sections 4.7 and 4.8 aiming to see which special cases of and +! satisfy the following properties: Aristotle’s Thesis, Simplification, Secondary Boethius, Transitivity, Contraposition, Monotonicity.
Keywords: Boethius’ Thesis, Aristotle’s Thesis, Connexive logic, Deontic logic, Strict implication, Aristotelian square, Conditionals, Paradoxes of implication, Law of identity, Consequential implication, Law of contraposition, Monotonicity.

Steltzner (1996) explains how the major employer in Frege's Jena was Zeiss Optics, with its visionary leader Carl Zeiss and Ernst Abbe, and how Frege was supported all of his life through anonymous donations from this source. Modern logic owes a lot to enlightened industrialists who wanted to give back to society.

En el año 1987 se publicó una demostración de la existencia de Dios extraída de los papeles del matemático y lógico austríaco Kurt Gödel. Este argumento prosigue la línea de pensamiento de los argumentos ontológicos de San Anselmo y Gottfried Leibniz, pero utilizando lógica modal de orden superior. No obstante, dicha demostración no está exenta de problemas y explicaremos cómo, en 2014, Christopher Benzmüller y Bruno Woltzenlogel arguyeron que los axiomas y definiciones del argumento de Gödel son inconsistentes.

ODS Statistical Graphics (or ODS Graphics for short) is major new functionality for creating statistical graphics that is available in a number of SAS software products, including SAS/STAT ® , SAS/ETS ® , SAS/QC ® , and SAS/GRAPH ®. With the production release of ODS Graphics in SAS 9.2, over sixty statistical procedures have been modified to use this functionality, and they now produce graphs as automatically as they produce tables. In addition, new procedures in SAS/GRAPH use this functionality to produce plots for exploratory data analysis and for customized statistical displays. SAS/GRAPH is required for ODS Graphics functionality in SAS 9.2. This paper presents the essential information you need to get started with ODS Graphics in SAS 9.2. ODS Graphics is an extension of ODS (the Output Delivery System), which manages procedure output and lets you display it in a variety of destinations, such as HTML and RTF. Consequently, many familiar features of ODS for tabular output apply equally to graphs. For statistical procedures that support ODS Graphics, you invoke this functionality with the ods graphics on statement. Graphs and tables created by these procedures are then integrated in your ODS output destination. ODS Graphics produces graphs in standard image file formats, and the consistent appearance and individual layout of these graphs are controlled by ODS styles and templates, respectively. Since the default templates for procedure graphs are provided by SAS, you do not need to know the details of templates to create statistical graphics. However, with some understanding of the underlying Graph Template Language, you can modify the default templates to make changes to graphs that are permanently in effect each time you run the procedure. Alternatively, to facilitate making immediate changes to a particular graph, SAS 9.2 introduces the ODS Graphics Editor, a point-and-click interface with which you can customize titles, annotate points, and make other enhancements.

St.lmmal~ tn reply to H. Bu~hoff's paper (this journal XII, 1981) I give another outline of Lakatos' approach to normative theories in order to reduce the misunderstandings Buflhoff seems to have fallen victim to. (1). In tJarticular, I try to show that he is wrong in claiming there is a vicious circle in this approach or my interpretation of it (2), Finally, I expose for criticism his alternative methodology of political science which propagates a theory of a ,,third type", suggesting that he takes too little seriously problems he calls academical although their importance has been shown not only by Lakatos but by political philosophers as Rawls and Nozick (3).

ODS Statistical Graphics (or ODS Graphics for short) is major new functionality for creating statistical graphics that is available in a number of SAS software products, including SAS/STAT ® , SAS/ETS ® , SAS/QC ® , and SAS/GRAPH ®. With the production release of ODS Graphics in SAS 9.2, over sixty statistical procedures have been modified to use this functionality, and they now produce graphs as automatically as they produce tables. In addition, new procedures in SAS/GRAPH use this functionality to produce plots for exploratory data analysis and for customized statistical displays. SAS/GRAPH is required for ODS Graphics functionality in SAS 9.2. This paper presents the essential information you need to get started with ODS Graphics in SAS 9.2. ODS Graphics is an extension of ODS (the Output Delivery System), which manages procedure output and lets you display it in a variety of destinations, such as HTML and RTF. Consequently, many familiar features of ODS for tabular output apply equally to graphs. For statistical procedures that support ODS Graphics, you invoke this functionality with the ods graphics on statement. Graphs and tables created by these procedures are then integrated in your ODS output destination. ODS Graphics produces graphs in standard image file formats, and the consistent appearance and individual layout of these graphs are controlled by ODS styles and templates, respectively. Since the default templates for procedure graphs are provided by SAS, you do not need to know the details of templates to create statistical graphics. However, with some understanding of the underlying Graph Template Language, you can modify the default templates to make changes to graphs that are permanently in effect each time you run the procedure. Alternatively, to facilitate making immediate changes to a particular graph, SAS 9.2 introduces the ODS Graphics Editor, a point-and-click interface with which you can customize titles, annotate points, and make other enhancements.

The logic of Conditional Beliefs has been introduced by Board, Baltag and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. It is shown that the semantics of this logic, defined in terms of plausibility models, can be equivalently formulated in terms of neighbourhood models, a multi-agent generalisation of Lewis' spheres models. On the base of this new semantics, a labelled sequent calculus for this logic is developed. The calculus has strong proof-theoretic properties, in particular cut and contraction are admissible and that the calculus provides a direct decision procedure for this logic. Further, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic.

We introduce a logic programming language which supports hypothetical and counterfactual reasoning. The language is based on a conditional logic which enables to formalize conditional updates of the knowledge base. Due to the presence of integrity constraints, alternative revisions of the knowledge base may result from an update. We develop an abductive semantics which captures dierent evolutions of the knowledge base. Furthermore, we provide a goal-directed abductive proof procedure to compute the alternative solutions for a goal. We ®nally analyze our conditional programming language in the context of belief revision theory, and we establish a connection with Nebel's prioritized base revision.

We reformulate AGM postulates for belief revision systems that may contain conditional formulas. We show that we can establish a mapping between belief revision systems and conditionals by means of the so called Ramsey Test, without incurring Gärdenfors triviality result. We then derive the conditional logic BCR from our revision postulates by means of a strong version of the Ramsey Test. We give a sound and complete axiomatization of this logic with respect to its standard selection-function models semantics, and we prove its decidability. We finally show that there is an isomorphism between belief revision systems and selection function models of BCR via a representation theorem. The logic BCR provides a logical formalization of belief revision in the language of conditional logic.

In this paper we propose a conditional logic IBCto represent iterated belief revision. We define an iterated belief revision system by strengthening the postulates proposed by Darwiche and Pearl [3]. First, following the line of Darwiche and Pearl, we modify AGM postulates to make belief revision a function of epistemic states rather than of belief sets. Then we propose a set of postulates for iterated revision which, together with the (modified) AGM postulates, entail Darwiche and Pearl's ones. The conditional logic IBChas a standard semantics in terms of selection function models and provides a natural representation of epistemic states. IBCcontains conditional axioms, corresponding to the postulates for iterated revision. We provide a representation result, which establishes a one to one correspondence between iterated belief revision systems and IBC-models. We prove that Gärdenfors' Triviality Result does not apply to IBC.

This is the annual report for the Hydrogen Storage Engineering Center of Excellence project as required by DOE EERE's Fuel Cell Technologies Office. We have been provided with a specific format. It describes the work that was done with cryo-sorbent based and chemical-based hydrogen storage materials. Balance of plant components were developed, proof-of-concept testing performed, system costs estimated, and transient models validated as part of this work.

Default conditionals are statements that express a condition of normality, in the form 'if ϕ then normally ψ' and are of primary importance in Knowledge Representation. There exist modal approaches to the construction of conditional logics of normality. Most of them are built on notions of preference among possible worlds, corresponding to the semantic intuition that (ϕ ⇒ ψ) is true in a situation if in the most preferred (most 'normal') situations in which ϕ is true, ψ is also true. It has been noticed that there exist natural epistemic readings of a default conditional, but this direction has not been thoroughly explored. A statement of the form 'something known to be a bird, that can be consistently believed to fly, does fly' involves well-known epistemic attitudes and allows the possibility of defining defaults within the rich framework of Epistemic Logic. We pursue this direction here within KBE, a recently introduced S4.2-based modal logic of knowledge, belief and estimation. In this logic, knowledge is a normal S4 operator, belief is a normal KD45 operator and estimation is a non-normal operator interpreted as a 'majority' quantifier over the set of epistemically alternative situations. We define and explore various conditionals using the epistemic operators of KBE, capturing (ϕ ⇒ ψ) in various ways, including 'it is known that assuming ϕ allows us to assume ϕ ∧ ψ' or 'if ϕ is known and there is no reason to believe ¬ψ then ψ can be plausibly inferred'. Overall, we define here two weak nonmonotonic default conditionals, one monotonic conditional and two stronger nonmonotonic conditionals without axiom ID. Our results provide concrete evidence that the machinery of epistemic logic can be exploited for the study of default conditionals.

The Output Delivery System (ODS) delivers what used to be printed output in many convenient forms. What most of us don't realize is that "printed output" from procedures (whether the destination is PDF, RTF, or HTML) is the result of SAS® packaging a collection of items that come out of a procedure that most people want to see in a predefined order (aka template.) With tools such as ODS TRACE, PROC CONTENTS and PROC PRINT, this paper explores the many buried treasures of procedural output and ODS output objects and demonstrates how to use these objects to get exactly the information that is needed, in exactly the format wanted. INFORMATION OVERLOAD SAS procedures can convey an enormous amount of information-sometimes more information than is needed. By manipulating procedural output and ODS output objects, we can pick and choose just the information we want to see. We can then harness the power of SAS reporting procedures to present the information accurately and attractively. Two full sample programs, one designed to be run interactively, and one designed to be run in batch mode, are provided in a zip file in the proceedings. These programs use the SASHELP.CLASS data set provided with SAS software. Code snippets are provided in the text of the paper.

Seit einiger Zeit werden wissenschaftstheoretische Behauptungen zunehmend dutch wissenschaftshistorische Hinweise gesttitzt oder bestritten. Die vorliegenden Ans~itze (etwa bei Kuhn und Lakatos) zu einer methodologischen Reflexion au£ dieses Verfah-~ahren sind abet unznreichend. Eine genauere logische Analyse zeigt, dab wissenschaftshistorische Begrtindungen wissenschaftstheoretischer Behauptungen spezielte Formen praktischer Syllogismen sind trod dab die Zul•ssigkeit derartiger Begrtindungen nicht nut yon der Gtiltigkeit praktischer Syllogismen abhfingt, sondern auch yon der Feststellbarkeit des Erkennmisfortschritts sowie yon der Rechdertigung wissenschaftshistorischer Aussagen unabh~ngig yon alien erst noch zu prafenden methodologischen Modellen.

We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our proposal applies the multi-type methodology in the design of display calculi, starting from a semantic analysis based on the translation from monotonic modal logic to normal bi-modal logic.

We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our proposal applies the multi-type methodology in the design of display calculi, starting from a semantic analysis based on the translation from monotonic modal logic to normal bi-modal logic.

The notion of comparative similarity 'X is more similar or closer to Y than to Z' has been investigated in both foundational and applied areas of knowledge representation and reasoning, e.g., in concept formation, similarity-based reasoning and areas of bioinformatics such as protein sequence alignment. In this paper we analyse the computational behaviour of the 'propositional' logic with the binary operator 'closer to a set τ1 than to a set τ2' and nominals interpreted over various classes of distance (or similarity) spaces. In particular, using a reduction to the emptiness problem for certain tree automata, we show that the satisfiability problem for this logic is ExpTime-complete for the classes of all finite symmetric and all finite (possibly non-symmetric) distance spaces. For finite subspaces of the real line (and higher dimensional Euclidean spaces) we prove the undecidability of satisfiability by a reduction of the solvability problem for Diophantine equations. As our 'closer' operator has the same expressive power as the standard operator > of conditional logic, these results may have interesting implications for conditional logic as well.

We propose and investigate a uniform modal logic framework for reasoning about topology and relative distance in metric and more general distance spaces, thus enabling the comparison and combination of logics from distinct research traditions such as Tarski's S4 for topological closure and interior, conditional logics, and logics of comparative similarity. This framework is obtained by decomposing the underlying modal-like operators into first-order quantifier patterns. We then show that quite a powerful and natural fragment of the resulting first-order logic can be captured by one binary operator comparing distances between sets and one unary operator distinguishing between realised and limit distances (i.e., between minimum and infimum). Due to its greater expressive power, this logic turns out to behave quite differently from both S4 and conditional logics. We provide finite (Hilbert-style) axiomatisations and ExpTime-completeness proofs for the logics of various classes of distance spaces, in particular metric spaces. But we also show that the logic of the real line (and various other important metric spaces) is not recursively enumerable. This result is proved by an encoding of Diophantine equations.

Categorisation of objects into classes is currently supported by (at least) two 'orthogonal' methods. In logic-based approaches, classifications are defined through ontologies or knowledge bases which describe the existing relationships among terms. Description logic (DL) has become one of the most successful formalisms for representing such knowledge bases, in particular because theoretically well-founded and efficient reasoning tools have been readily available. In numerical approaches, classifications are obtained by first computing similarity (or proximity) measures between objects and then categorising them into classes by means of Voronoi tessellations, clustering algorithms, nearest neighbour computations, etc. In many areas such as bioinformatics, computational linguistics or medical informatics, these two methods have been used independently of each other: although both of them are often applied to the same domain (and even by the same researcher), up to now no formal interaction mechanism has been developed. In this paper, we propose a DL-based integration of the two classification methods. Our formalism, called SL + ALCQIO, extends the expressive DL ALCQIO by means of the constructors of the similarity logic SL which allow definitions of concepts in terms of both comparative and absolute similarity. In the combined knowledge base the user should declare the similarity spaces where the new operators are interpreted. Of course, SL + ALCQIO can only be useful if classifications with this logic are supported by automated reasoning tools. We lay theoretical foundations for the development of such tools by showing that reasoning problems for SL + ALCQIO can be decomposed into the corresponding problems for its DL-part ALCQIO and similarity part SL. Then we investigate reasoning in SL and prove that consistency and many other reasoning problems are ExpTime-complete for this logic. Using this result and a recent complexity result of Pratt-Hartmann for ALCQIO, we prove that reasoning in SL + ALCQIO is NExpTime-complete. As the 'closer' operator of SL has the same expressive power as the standard implication > of conditional logic, these results may have interesting consequences for conditional logic as well.

Obligations can be affected by knowledge. Several approaches exist to formalize knowledge-based obligations, but no formalism has been developed yet to capture the dynamic interaction between knowledge and obligations. We introduce the dynamic extension of an existing logic for knowledge-based obligations here. We motivate the logic by analyzing several scenarios and by showing how it can capture in an original manner several fundamental deontic notions such as absolute, prima facie and allthings-considered obligations. Finally, in the dynamic epistemic logic tradition, we provide reduction axioms for the dynamic operator of the new logic.

The aim of this paper is to argue for a revised and precisified version of the infamous Verifiability Criterion for the meaningfulness of declarative sentences. The argument is based on independently plausible premises concerning probabilistic confirmation and meaning as context-change potential, it is shown to be logically valid, and its ramifications for potential applications of the criterion are being discussed. Although the paper is not historical but systematic, the criterion thus vindicated will resemble the original one(s) in some important ways. At the same time, it will also be more modest insofar as meaningfulness will turn out to be relativized linguistically and probabilistically, and different choices of the linguistic and probabilistic parameters may lead to different verdicts on meaningfulness.

This paper reports completeness results for dyadic deontic logics in the tradition of Hansson's systems. There are two ways to understand the core notion of best antecedentworlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different versions of the so-called limit assumption. Four of them are disentangled, and compared. The main observation of this paper is that, even in the partial order case, the contrast between maximality and optimality is not as significant as one could expect, because the logic remains the same whatever notion of best is used. This is established by showing that, given analogous properties for the betterness relation, the same system is sound and complete with respect to its intended modelling. The chief result of this paper concernsÅqvist's system F supplemented with the principle (CM) of cautious monotony. It is established that, under the maximality rule, F+(CM) is sound and complete with respect to the class of models in which the betterness relation is required be reflexive and smooth (for maximality). From this, a number of spin-off results are obtained. First and foremost, it is shown that a similar determination result holds for optimality; that is, under the optimality rule, F+(CM) is also sound and complete with respect to the class of models in which the betterness relation is reflexive and smooth (for optimality). Other spin-off results concern classes of models in which further constraints are placed on the betterness relation, like totalness and transitivity.

A framework and methodology-termed LogiKEy-for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples-all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.