the periodic table of elementary particles
... All leptons, quarks, and gauge bosons can be placed in the periodic table of elementary particles. The periodic table is derived from dualities of string theory and a Kaluza-Klein substructure for the six extra spatial dimensions. As a molecule is the composite of atoms with chemical bonds, a hadron ...
... All leptons, quarks, and gauge bosons can be placed in the periodic table of elementary particles. The periodic table is derived from dualities of string theory and a Kaluza-Klein substructure for the six extra spatial dimensions. As a molecule is the composite of atoms with chemical bonds, a hadron ...
Chiron: A Set Theory with Types, Undefinedness, Quotation, and
... The usefulness of a logic is often measured by its expressivity: the more that can be expressed in the logic, the more useful the logic is. By a logic, we mean a language (or a family of languages) that has a formal syntax and a precise semantics with a notion of logical consequence. (A logic may al ...
... The usefulness of a logic is often measured by its expressivity: the more that can be expressed in the logic, the more useful the logic is. By a logic, we mean a language (or a family of languages) that has a formal syntax and a precise semantics with a notion of logical consequence. (A logic may al ...
Logic 1 Lecture Notes Part I: Propositional Logic
... constants or propositional atoms. Some also call them propositional variables, but this latter expression is bad terminology, since, as we will see in the section on semantics for propositional logic, their interpretation does not vary within a particular truth value assignment, and hence they do no ...
... constants or propositional atoms. Some also call them propositional variables, but this latter expression is bad terminology, since, as we will see in the section on semantics for propositional logic, their interpretation does not vary within a particular truth value assignment, and hence they do no ...
On the Question of Absolute Undecidability
... discrete topology on ω. As a topological space ω ω is homeomorphic to the standard space of irrationals. In addition to this space we will also be interested in the n-dimensional product spaces (ω ω )n . Given a subset A of (ω ω )n+1 the complement of A is just the set of elements not in A and the p ...
... discrete topology on ω. As a topological space ω ω is homeomorphic to the standard space of irrationals. In addition to this space we will also be interested in the n-dimensional product spaces (ω ω )n . Given a subset A of (ω ω )n+1 the complement of A is just the set of elements not in A and the p ...
axioms
... • Note: It is true that we also produced a “non-model” (the books-shelves model) but this does not imply the system is not consistent. ...
... • Note: It is true that we also produced a “non-model” (the books-shelves model) but this does not imply the system is not consistent. ...
Modal logic and the approximation induction principle
... from the richest characterizations, which correspond to the canonical process equivalences, there are also finitary versions (denoted with a superscript ∗ ), which allow only conjunctions over a finite set. Intermediate equivalences based on formulas with arbitrary conjunctions but of finite depth a ...
... from the richest characterizations, which correspond to the canonical process equivalences, there are also finitary versions (denoted with a superscript ∗ ), which allow only conjunctions over a finite set. Intermediate equivalences based on formulas with arbitrary conjunctions but of finite depth a ...
HKT Chapters 1 3
... with domain A and range B. The set of all functions f : A → B is denoted A → B or B A . A function can be specified anonymously with the symbol →. For example, the function x → 2x on the integers is the function Z → Z that doubles its argument. ...
... with domain A and range B. The set of all functions f : A → B is denoted A → B or B A . A function can be specified anonymously with the symbol →. For example, the function x → 2x on the integers is the function Z → Z that doubles its argument. ...
In terlea v ed
... are never executed at precisely the same instant, but take turns in executing atomic transitions. When one of the participating processes executes an atomic transition, the others are inactive. Thus, rather than input/output pairs, execution sequences of the atomic instructions of sequential process ...
... are never executed at precisely the same instant, but take turns in executing atomic transitions. When one of the participating processes executes an atomic transition, the others are inactive. Thus, rather than input/output pairs, execution sequences of the atomic instructions of sequential process ...
Proof Search in Modal Logic
... and the Logic of Provability (GL). An intercalation calculus ([10]) was used as the underlying logical calculus, and the proof search was automated using the theorem prover AProS [1]. The inference rules in the intercalation calculus for the systems S5 and GL, and their soundness and completeness re ...
... and the Logic of Provability (GL). An intercalation calculus ([10]) was used as the underlying logical calculus, and the proof search was automated using the theorem prover AProS [1]. The inference rules in the intercalation calculus for the systems S5 and GL, and their soundness and completeness re ...
From Syllogism to Common Sense Normal Modal Logic
... significantly shorten proofs, which is our main concern here. ‣ Example: Congruence rules. ‣ The general form of a rule is the following: ...
... significantly shorten proofs, which is our main concern here. ‣ Example: Congruence rules. ‣ The general form of a rule is the following: ...
Lecture Notes on Stability Theory
... i.e. Boolean combinations of algebraic sets. Th (M) is axiomatized as the theory of algebraically closed fields of char 0, denoted ACF0 . Note in particular that every definable subset of M is either finite, or cofinite. Theories satisfying this property are called strongly minimal. (2) Let M = (R, ...
... i.e. Boolean combinations of algebraic sets. Th (M) is axiomatized as the theory of algebraically closed fields of char 0, denoted ACF0 . Note in particular that every definable subset of M is either finite, or cofinite. Theories satisfying this property are called strongly minimal. (2) Let M = (R, ...
The Relative Efficiency of Propositional Proof
... for propositional proof systems which will be used in the rest of this paper. The letter n will always stand for an adequate set of propositional connectives which are binary, unary, or nullary (have two, one, or zero arguments). Adequate here means that every truth function can be expressed by form ...
... for propositional proof systems which will be used in the rest of this paper. The letter n will always stand for an adequate set of propositional connectives which are binary, unary, or nullary (have two, one, or zero arguments). Adequate here means that every truth function can be expressed by form ...
Pebble weighted automata and transitive - LSV
... In this section we set up the notation and we recall some basic results on weighted automata and weighted logics. We refer the reader to [6,7] for details. Throughout the paper, Σ denotes a finite alphabet and Σ + is the free semigroup over Σ, i.e., the set of nonempty words. The length of u ∈ Σ + i ...
... In this section we set up the notation and we recall some basic results on weighted automata and weighted logics. We refer the reader to [6,7] for details. Throughout the paper, Σ denotes a finite alphabet and Σ + is the free semigroup over Σ, i.e., the set of nonempty words. The length of u ∈ Σ + i ...
Introduction to Logic
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
Introduction to Logic
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
Pair production processes and flavor in gauge
... Doing so is the aim of this work. The main motivation is not that large deviations from the standard model are necessarily expected. In fact, as the following will show, deviations are probably restricted to very special circumstances, if at all. This is likely due to the particular structure of the ...
... Doing so is the aim of this work. The main motivation is not that large deviations from the standard model are necessarily expected. In fact, as the following will show, deviations are probably restricted to very special circumstances, if at all. This is likely due to the particular structure of the ...
Outlier Detection Using Default Logic
... property, denoted by a set of literals , holding in every extension of the theory. The exceptional property is the outlier witness for < . Thus, according to this defini tion, in the default theory of Example 1 above we should conclude that `pw y'{| ~ ...
... property, denoted by a set of literals , holding in every extension of the theory. The exceptional property is the outlier witness for < . Thus, according to this defini tion, in the default theory of Example 1 above we should conclude that `pw y'{| ~ ...
The Internal and External Problems of String Theory
... supersymmetric formulation of string theory it also included fermionic matter fields. Exclusively the fact that the quantized string has spin-2 states which can be interpreted as gravitons and which are completely unmotivated in the context of hadron physics led to this change of strategy and of con ...
... supersymmetric formulation of string theory it also included fermionic matter fields. Exclusively the fact that the quantized string has spin-2 states which can be interpreted as gravitons and which are completely unmotivated in the context of hadron physics led to this change of strategy and of con ...
First-Order Proof Theory of Arithmetic
... can prove the arithmetized version of the cut-elimination theorem and those which cannot; in practice, this is equivalent to whether the theory can prove that the superexponential function i 7→ 21i is total. The very weak theories are theories which do not admit any induction axioms. Non-logical sym ...
... can prove the arithmetized version of the cut-elimination theorem and those which cannot; in practice, this is equivalent to whether the theory can prove that the superexponential function i 7→ 21i is total. The very weak theories are theories which do not admit any induction axioms. Non-logical sym ...
First-Order Intuitionistic Logic with Decidable Propositional
... Recently, research in the area of combining features of classical and intuitionistic logic has shifted towards logics containing two different variants of connectives. One of them is intuitionistic, and the other is classical [Kr] Fibring logics is the most noticeable technique in this research [Ga] ...
... Recently, research in the area of combining features of classical and intuitionistic logic has shifted towards logics containing two different variants of connectives. One of them is intuitionistic, and the other is classical [Kr] Fibring logics is the most noticeable technique in this research [Ga] ...
Intermediate Logic
... almost every mathematical object can be seen as a set of some kind. In logic, as in other parts of mathematics, sets and set theoretical talk is ubiquitous. So it will be important to discuss what sets are, and introduce the notations necessary to talk about sets and operations on sets in a standard ...
... almost every mathematical object can be seen as a set of some kind. In logic, as in other parts of mathematics, sets and set theoretical talk is ubiquitous. So it will be important to discuss what sets are, and introduce the notations necessary to talk about sets and operations on sets in a standard ...
possible-worlds semantics for modal notions conceived as predicates
... belief, future and past truth, obligation and other modalitities should be formalised by operators or by predicates was a matter of dispute up to the early sixties between two almost equally strong parties. Then two technical achievements helped the operator approach to an almost complete triumph ov ...
... belief, future and past truth, obligation and other modalitities should be formalised by operators or by predicates was a matter of dispute up to the early sixties between two almost equally strong parties. Then two technical achievements helped the operator approach to an almost complete triumph ov ...
Introduction to Logic
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
... The term “logic” may be, very roughly and vaguely, associated with something like “correct thinking”. Aristotle defined a syllogism as “discourse in which, certain things being stated something other than what is stated follows of necessity from their being so.” And, in fact, this intuition not only ...
File
... The usual connectives ‘and’, ‘or’ and ‘but’ used in English language are not precise and unambiguous. Since we need a precise language with exact connective, we will not symbolize the above conjunctions in our object language. However we use connectives, which have some resemblance to the connective ...
... The usual connectives ‘and’, ‘or’ and ‘but’ used in English language are not precise and unambiguous. Since we need a precise language with exact connective, we will not symbolize the above conjunctions in our object language. However we use connectives, which have some resemblance to the connective ...
A VIEW OF MATHEMATICS Alain CONNES Mathematics is the
... It is also vital to always keep moving. The risk otherwise is to confine oneself in a relatively small area of extreme technical specialization, thus shrinking one’s perception of the mathematical world and of its bewildering diversity. The really fundamental point in that respect is that while so m ...
... It is also vital to always keep moving. The risk otherwise is to confine oneself in a relatively small area of extreme technical specialization, thus shrinking one’s perception of the mathematical world and of its bewildering diversity. The really fundamental point in that respect is that while so m ...