Against Metaphysical Egalitarianism

Preface to Second Edition. Preface to Revised Edition. Acknowledgments. Introduction. 1. A Brief Introduction to Key Terms. 1.1 Arguments. 1.2 Putting Arguments into a Standard Format. 1.3 Multiple Conclusions. 1.4 Deductive Validity. 1.5 Soundness. 1.6 Missing Premises and Conclusions. 2. Argument Forms and Propositional Logic. 2.1 Formal Validity. 2.2 Quotation Marks. 2.3 Metalinguistic Variables. 2.4 Non-formal Validity. 2.5 The Need for Propositional Logic. 2.6 The Type/Token Distinction. 3. Conjunction. 3.1 Logical Conjunction. 3.2 Distinguishing Deductive from Non-deductive Aspects of Conjunction. 3.3 Phrasal Logical Conjunctions. 3.4 Series Decompounding. 3.5 Using 'Respectively'. 3.6 Symbolizing Logical Conjunctions. 4. Negation. 4.1 Logical Negation. 4.2 Some Other Negative Expressions. 4.3 A Point about Methodology. 4.4 A Point on Ambiguity. 4.5 Symbolizing Logical Negations. 4.6 Ambiguity and the Need for Groupers. 4.7 Review of Symbols. 4.8 Using 'Without'. 4.9 Argument Forms Continued. 4.10 Symbolizing Logical Negations Continued. 5. Truth Tables. 5.1 Well-formed Formulas. 5.2 Scope. 5.3 Main Connective. 5.4 Truth Tables. 6. Disjunction. 6.1 Logical Disjunction. 6.2 Disjunction and Negation. 6.3 Iterations and Groupers. 6.4 Inclusive versus Exclusive 'Or'. 6.5 Symbolizing Logical Disjunctions Continued. 7. Conditionals. 7.1 Conditionals with Constituent Statements. 7.2 Conditionals without Constituent Statements. 7.3 Logical Conditionals. 7.4 Symbolizing Conditionals in PL. 7.5 Necessary and Sufficient Conditions. 7.6 Only If. 7.7 Unless. 7.8 Since, Because. 7.9 Conditionals and Groupers. 7.10 If and Only If. 7.11 A Revised Grammar for Well-formedness in PL. 7.12 Summarizing Truth Tables. 8. Truth Trees. 8.1 Reviewing Validity. 8.2 Tree Trunks and Compound and Atomic Statements. 8.3 Truth Tree Rules. 8.4 Strategies. 8.5 Truth Trees and Invalidity. 8.6 Propositional Logic and Counter-examples (Counter-models). 8.7 Logical Properties and Relations Revisited. 9. Property Predicate Logic. 9.1 Limits of Propositional Logic. 9.2 Singular Terms. 9.3 Property Predicates. 9.4 Quantifiers. 9.5 Complex Predicates. 9.6 Well-formedness in PPL. 9.7 Quantifiers Modifying General Terms. 10. Evaluating Arguments in Property Predicate Logic. 10.1 Quantifiers and Scope. 10.2 The Truth Tree Method Extended. 10.3 Super Strategy. 10.4 Property Predicate Logic and Counter-examples (Counter-models). 10.5 PPL Logical Equivalences and Non-equivalences. 10.6 Other Logical Properties and Relations. 11. Property Predicate Logic Refinements. 11.1 Literal Meaning. 11.2 'Any' as an Existential. 11.3 Restrictive Relative Clauses. 11.4 Pronouns Revisited. 11.5 Only. 11.6 Restrictive Words in English. 11.7 Evaluating Symbolizations of English in Logical Notation. 12. Relational Predicate Logic. 12.1 Limits of Property Predicate Logic. 12.2 Convention 1: Number. 12.3 Convention 2: Order. 12.4 Convention 3: Active/Passive Voice. 12.5 Convention 4: Single Quantifiers. 12.6 Variables. 13. Relational Predicate Logic with Nested Quantifiers. 13.1 Multiply General Statements. 13.2 Universal Quantifier Procedure. 13.3 Existential Quantifier Procedure. 13.4 Double Binding Variables. 13.5 Systematic and Analytic Procedures. 13.6 A Grammar for Well-formedness in RPL. 13.7 Nested Quantifiers, Variables, and Scope. 13.8 Order and Scope Refinements. 13.9 Summary of the Overall Procedure for Symbolizing English Statements with Nested Quantifiers into RPL. 14. Extending the Truth Tree Method to RPL. 14.1 RPL Arguments without Quantifiers. 14.2 RPL Arguments without Nested Quantifiers. 14.3 RPL Arguments with Nested Quantifiers. 14.4 Choosing Singular Terms to Instantiate. 14.5 Infinite Truth Trees for RPL Arguments. 14.6 Summary of Truth Tree Strategies. 14.7 Relational Predicate Logic and Counter-Examples (Counter-Models). 15. Negation, Only, and Restrictive Relative Clauses. 15.1 Negation. 15.2 'Only' as a Quantifier. 15.3 Restrictive Relative Clauses. 15.4 Quantifiers and Anaphora. 15.5 Anaphora and Restrictive Relative Clauses. 15.6 Anaphora across sentences. 15.7 Quantification in English. 16. Relational Predicate Logic with Identity. 16.1 Limits of Relational Predicate Logic. 16.2 Extending the Truth Tree Method to RPL. 16.3 Sameness and Distinctness in English. 16.4 Numerical Adjectives. 16.5 Definite Descriptions. 17. Verbs and their Modifiers. 17.1 Prepositional Phrases. 17.2 The Event Approach. 17.3 Indirect Support of the Event Approach. 17.4 Adverbial Modification. 17.5 Problems with the Event Approach. Appendix. A1 Conjunction. A2 Negation and Disjunction. A3 Conditionals. A4 Property Predicate Logic. A5 Relational Predicate Logic. A6 Relational Predicate Logic with Identity. A7 Verbs and their Modifiers. Answers for Selected Exercises. Logical Symbols. Index.

This paper outlines a structuring and integration of two formalisms of knowledge representation: FRAMES AND RULES. The procedure is based on the concepts of these formalisms. For that, an Abelian Group Structure is obtained defining a particular internal operation on the set of FRAMES. Then two operations in the set of RULES are defined. These operations are based on the logical conjunctions as well as logical disjunctions. Fulfilling that the Rules with these defined operations are a Field. Finally an external operation of the set of Rules by the set of frames in the set of frames is defined by verifying the properties of Vectorial Space.

Public-key encryption with keyword search (PEKS) is a cryptographic primitive that allows us to search encrypted data for those of including particular keywords without decrypting them. PEKS is expected to be used for enhancing security of cloud storages. It is known that PEKS can be constructed from anonymous identity-based encryption (IBE), anonymous attribute-based encryption (ABE) and so on. It is believed that it is difficult to construct PEKS schemes that can specify a flexible search condition such as logical disjunctions and logical conjunctions from weaker cryptographic tools than ABE. However, this intuition has not been rigorously justified. In this paper, we formally prove it by constructing key-policy ABE from PEKS for monotone boolean formulas.

Public-key encryption with keyword search (PEKS) is a cryptographic primitive that allows us to search encrypted data for those of including particular keywords without decrypting them. PEKS is expected to be used for enhancing security of cloud storages. It is known that PEKS can be constructed from anonymous identity-based encryption (IBE), anonymous attribute-based encryption (ABE) and so on. It is believed that it is difficult to construct PEKS schemes that can specify a flexible search condition such as logical disjunctions and logical conjunctions from weaker cryptographic tools than ABE. However, this intuition has not been rigorously justified. In this paper, we formally prove it by constructing key-policy ABE from PEKS for monotone boolean formulas.

The theory of metric spaces is a convenient and very powerful way of examining the behavior of numerous mathematical models. In a previous paper, a new operation between functions on a compact real interval called fractal convolution has been introduced. The construction was done in the framework of iterated function systems and fractal theory. In this article we extract the main features of this association, and consider binary operations in metric spaces satisfying properties as idempotency and inequalities related to the distance between operated elements with the same right or left factor (side inequalities). Important examples are the logical disjunction and conjunction in the set of integers modulo 2 and the union of compact sets, besides the aforementioned fractal convolution. The operations described are called in the present paper convolutions of two elements of a metric space E. We deduce several properties of these associations, coming from the considered initial conditions. Thereafter, we define self-operators (maps) on E by using the convolution with a fixed component. When E is a Banach or Hilbert space, we add some hypotheses inspired in the fractal convolution of maps, and construct in this way convolved Schauder and Riesz bases, Bessel sequences and frames for the space.

Programming in Three Dimensions

Genuine Paraconsistent logics $$\mathbf {L3A}$$ and $$\mathbf {L3B}$$ were defined in 2016 by Beziau et al, including only three logical connectives, namely, negation disjunction and conjunction. Afterwards in 2017 Hernandez-Tello et al, provide implications for both logics and define the logics $$\mathbf {L3A_G}$$ and $$\mathbf {L3B_G}$$ . In this work we continue the study of these logics, providing sound and complete Hilbert-type axiomatic systems for each logic. We prove among other properties that $$\mathbf {L3A_G}$$ and $$\mathbf {L3B_G}$$ satisfy a restricted version of the Substitution Theorem, and that both of them are maximal with respect to Classical Propositional Logic. To conclude we make some comparisons between $$\mathbf {L3A_G}$$ and $$\mathbf {L3B_G}$$ and among other logics, for instance $${\mathbf {Int}}$$ and some $${\mathbf {LFI}}$$ s.

An S-box is a non-linear transformation that takes n bits as input and returns m bits. This transformation is most easily represented as a nm lookup table. Most often, only balanced S-boxes are used in cryptography. This means that the number of input bits is equal to the number of output bits. The S-box is an important part of most symmetric ciphers. The selection of the correct substitution makes the link between the key and the ciphertext more complex (non-linear), which makes it much more difficult to hack. This paper deals with a hardware implementation of S-boxes. This implementation can be realized by using logical conjunction, disjunction, negation and delay blocks. The main indicator of productivity of such implementations is a circuit depth, namely the maximum length of a simple way of the circuit and a circuit complexity, namely the quantity of logic elements (negation elements are not taken into account). The article considers the standard synthesis methods (based on DNF, Shannon, Lupanov), proposes a new algorithm to minimize the complexity of an arbitrary Boolean functions system and a way to reduce the complexity of the circuit obtained after simplification by the ESPRESSO algorithm of DNF of the function related to the output of the S-box. To compare the efficiency of the methods, the C++ program was created that generates a circuit in the Verilog language. The estimates of depth and complexity are obtained for the schemes produced as a result of the programs operation. The article ends with a comparison of the efficiency of S-box schemes of known cryptographic standards obtained as the output of the program (with each other and with the result of the Logic Friday program).

Complete and Absolute temporal knowledge is usually not always available for many knowledge based systems, notably in the domain of Artificial Intelligence. Based on a time theory that takes both points and intervals as primitive, this paper introduces a graphical representation for uncertain and incomplete temporal knowledge, which allows logical expressions of both absolute and relative temporal relations, including both logical conjunctions and disjunctions. The consistency of any given collection of uncertain and incomplete temporal knowledge depends on if there is at one temporal scenario that is temporal consistent, where a consistency checker for temporal scenarios is provided.

Formal concept analysis (FCA) and description logics (DLs) are two major formalisms around concepts. However, concepts in FCA and concepts in DLs are of different nature. The former are tuples/properties pairs in a given relation, the later are just subsets of domains in terminological interpretations. To represent the logical difference of tuples and attribute values in relations, a dual description logic (DDL) is introduced, in which constants are classified into two classes: tuple constants and value constants, and they are interpreted into two disjoint parts in domain, respectively. Given a model M for DDL, we can obtain a normal relation RM. This paper demonstrates how to connect FCA-concepts in RM and concepts in DDL. To do so, we introduce logical operations negation, disjunction and conjunction on values and on attribute-value pairs, and then build Φ-statements from attribute-value pairs inductively with these operations, and further define a kind of extended FCA-concepts, called Γ-concepts. Each Γ-concept consists of two parts: the extent (tuples the concept covers) and the intent (Φ-statements describing the concept), and there are the following results: the union of any number of extents is always an extent; the complement of an extent is always an extent. Consequently, we obtain two isomorphic lattices: one is LM=(Θ, ∪,∩,–), which is the lattice of subsets of Θ, and the other is concept lattice L(↑RM), where Θ consists of the interpretations of DDL-concepts, and ↑RM is an extend relation from the normal relation RM.

We investigate the subsumption problem in logic-based knowledge representation languages of the KL-ONE family and give decision procedures. All our languages contain as a kernel the logical connectives conjunction, disjunction, and negation for concepts, as well as role quantification. The algorithms are rule-based and can be understood as variants of tableaux calculus with a special control strategy. In the first part of the paper, we add number restrictions and conjunction of roles to the kernel language. We show that subsumption in this language is decidable, and we investigate sublanguages for which the problem of deciding subsumption is PSPACE-complete. In the second part, we amalgamate the kernel language with feature descriptions as used in computational linguistics. We show that feature descriptions do not increase the complexity of the subsumption problem.

Summary Models of simple deductions with three logical rules, conjunction, disjunction, and implication were proposed, from which patterns of reaction-times in deductive reasoning were constructed. Thirty-five male and female undergraduate Ss were asked to draw inferences from abstract logical rules based on Wason's and Johnson-Laird's selection task. For all rules, it was predicted that trials on which a fallacious inference was invited but refused would show the shortest latencies, while valid inferences involving memory retrieval would require more time, with the longest latencies occurring on inferences requiring memory retrieval and negation of retrieved information. In general, the data supported the predictions. Time for rule encoding was also measured, and it was found that disjunction takes longer to understand than implication or conjunction.

From the two-valued logic to fuzzy logic, proposition logic obtains a rapid development. This paper aims to construct a new kind os proposition logic form with the value of connection number. With the basic method of fuzzy logic, the value of proposition in the form of rough connection degree is obtained, and the three logical operators, disjunction, conjunction and negation are constructed. The three logical operators meet the seven rules of Involution, Idempotent, Exchange, Combination, Distribution, Absorption, and Morgan. It is proved that the algebra constructed by the three operators is soft algebra.

The most elementary logical system of some practical interest is the propositional logic. In this system is it possible to express logical consequences, conjunction, disjunction, and negation of propositions.

To signal a conjunction of many inputs negative regulation is likely