Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... The fourth principle analyzes disjunctions in terms of conjunctions in preference expressions. For instance, if I prefer flying to taking either a bus or a train, then I prefer flying to taking a bus, and I prefer flying to taking a train. This requirement seems natural, and we will see below that i ...
... The fourth principle analyzes disjunctions in terms of conjunctions in preference expressions. For instance, if I prefer flying to taking either a bus or a train, then I prefer flying to taking a bus, and I prefer flying to taking a train. This requirement seems natural, and we will see below that i ...
... Note that this definition is language-sensitive, in the sense that it matters what the possible substitution instances are. This is one type of inference considered in the literature. In this paper, we call this validity inference (with respect to 9). Some standard rules such as universal generaliza ...
From Parametricity to Conservation Laws, via Noether`s Theorem
... their type system by embedding it within System Fω. The benefits of this embedding are twofold. Firstly, by using the richer typelevel structure of System Fω, we can easily add useful indexed types like length indexed vectors and smooth function types, both of which would have required special treat ...
... their type system by embedding it within System Fω. The benefits of this embedding are twofold. Firstly, by using the richer typelevel structure of System Fω, we can easily add useful indexed types like length indexed vectors and smooth function types, both of which would have required special treat ...
THE SEMANTICS OF MODAL PREDICATE LOGIC II. MODAL
... more sophisticated notion of a modal individual and identity-at-a-world. It remains unsatisfactory having to choose between these competing semantics. Moreover, it would be nice if the difference between these semantics was better understood. Certainly, much research has been done into standard sema ...
... more sophisticated notion of a modal individual and identity-at-a-world. It remains unsatisfactory having to choose between these competing semantics. Moreover, it would be nice if the difference between these semantics was better understood. Certainly, much research has been done into standard sema ...
Gödel incompleteness theorems and the limits of their applicability. I
... (see [2]), whose proclaimed objective was to establish the consistency of mathematics (analysis and set theory) by using finitary tools. This problem was regarded by the representatives of Hilbert’s school as the central problem of mathematical logic. However, it follows from Gödel’s second theorem ...
... (see [2]), whose proclaimed objective was to establish the consistency of mathematics (analysis and set theory) by using finitary tools. This problem was regarded by the representatives of Hilbert’s school as the central problem of mathematical logic. However, it follows from Gödel’s second theorem ...
Automata-Theoretic Model Checking Lili Anne Dworkin Advised by Professor Steven Lindell
... class of formal methods, which are mathematical approaches to the development of hardware and software systems. Formal methods provide engineers with rigorous techniques for the analysis of systems. Thus, these methods are often employed when the correctness of a system is of particular importance. ...
... class of formal methods, which are mathematical approaches to the development of hardware and software systems. Formal methods provide engineers with rigorous techniques for the analysis of systems. Thus, these methods are often employed when the correctness of a system is of particular importance. ...
LTL and CTL - UT Computer Science
... inductively defined as follows: • if p ∈ AP then p is a valid LTL formula. • if ψ, φ are valid LTL formulas, then ¬ψ, ψ ∨ φ, Xψ, ψUφ are valid LTL formulas. We have now defined the syntax for LTL. Note that we use only the X and U modalities for defining the valid formulas in LTL. We will define the ...
... inductively defined as follows: • if p ∈ AP then p is a valid LTL formula. • if ψ, φ are valid LTL formulas, then ¬ψ, ψ ∨ φ, Xψ, ψUφ are valid LTL formulas. We have now defined the syntax for LTL. Note that we use only the X and U modalities for defining the valid formulas in LTL. We will define the ...
Semiconductor Physics Sectional Programme Overview
... sensitivity of our technique (photoelectron escape depth 0.5 nm) yields information essentially on the composition of the growth front. Our data clearly demonstrate that the surface composition of the dots is neither pure InAs nor homogeneous Inx Ga1−x As, but we observe an In concentration gradient ...
... sensitivity of our technique (photoelectron escape depth 0.5 nm) yields information essentially on the composition of the growth front. Our data clearly demonstrate that the surface composition of the dots is neither pure InAs nor homogeneous Inx Ga1−x As, but we observe an In concentration gradient ...
The Foundations
... is true ? => The proposition:” It_is_raining” is true iff the condition (or fact) that the sentence is intended to state really occurs(happens, exists) in the situation which the proposition is intended to describe. =>Example: Since it is not raining now(the current situation), the statement It_is_r ...
... is true ? => The proposition:” It_is_raining” is true iff the condition (or fact) that the sentence is intended to state really occurs(happens, exists) in the situation which the proposition is intended to describe. =>Example: Since it is not raining now(the current situation), the statement It_is_r ...
Equivalence for the G3'-stable models semantics
... which two programs are strongly G03 -equivalent also guarantee that two disjunctive programs are strongly equivalent in the p-stable semantics. We present two main results that guarantee G03 strong equivalence, one for two arbitrary programs and another one for a couple of programs of the form P , P ...
... which two programs are strongly G03 -equivalent also guarantee that two disjunctive programs are strongly equivalent in the p-stable semantics. We present two main results that guarantee G03 strong equivalence, one for two arbitrary programs and another one for a couple of programs of the form P , P ...
1. Propositional Logic 1.1. Basic Definitions. Definition 1.1. The
... “cut-free”), which consists of the rules of Pc other than Cut, and prove cutelimination—that every proof in Pc can be converted to one in Pcf c —and speed-up—that there are sequences which have short deductions in Pc , but have only very long deductions in Pcf c . Among other things, this will tell ...
... “cut-free”), which consists of the rules of Pc other than Cut, and prove cutelimination—that every proof in Pc can be converted to one in Pcf c —and speed-up—that there are sequences which have short deductions in Pc , but have only very long deductions in Pcf c . Among other things, this will tell ...
Counterfactuals
... If Jon had fired as soon as he saw Tom, Jon would have lived. If Tom had been wearing body armor, however, Jon would still not have lived. Translating these with φ as ‘Jon had fired as soon as he saw Tom’, φ0 as ‘Tom had been wearing body armor’, and ψ as ‘Jon would have lived’, we have both: φψ (φ ...
... If Jon had fired as soon as he saw Tom, Jon would have lived. If Tom had been wearing body armor, however, Jon would still not have lived. Translating these with φ as ‘Jon had fired as soon as he saw Tom’, φ0 as ‘Tom had been wearing body armor’, and ψ as ‘Jon would have lived’, we have both: φψ (φ ...
LHC Theory Lecture 1: Calculation of Scattering Cross Sections
... Proton-proton collider: bunches of protons are brought to collision at a center of mass (cms) energy of several TeV /c 2 (Tera ≡ T = 1012 ). About 115 billion particles per bunch of ∼ 7cm length and the diameter of a hair! As protons are very small objects (6 o of about 1fm=10−15 m), nearly all part ...
... Proton-proton collider: bunches of protons are brought to collision at a center of mass (cms) energy of several TeV /c 2 (Tera ≡ T = 1012 ). About 115 billion particles per bunch of ∼ 7cm length and the diameter of a hair! As protons are very small objects (6 o of about 1fm=10−15 m), nearly all part ...
Kuhn Losses Regained: Van Vleck from Spectra to
... By the time he wrote his article in Chemical Reviews, Van Vleck had come to recognize that a strong argument against the old and in favor of the new quantum theory could be found in the theory of susceptibilities, a subject of marginal interest during the reign of the old quantum theory. As he wrot ...
... By the time he wrote his article in Chemical Reviews, Van Vleck had come to recognize that a strong argument against the old and in favor of the new quantum theory could be found in the theory of susceptibilities, a subject of marginal interest during the reign of the old quantum theory. As he wrot ...
Relevant Logic A Philosophical Examination of Inference Stephen Read February 21, 2012
... ular, to specify some meaning-connection between premises and conclusion which can act as a sieve on the classically valid inferences. The present approach, however, directly replaces the Classical Account with the Relevant Account, and extracts the notion of relevance from the new criterion for val ...
... ular, to specify some meaning-connection between premises and conclusion which can act as a sieve on the classically valid inferences. The present approach, however, directly replaces the Classical Account with the Relevant Account, and extracts the notion of relevance from the new criterion for val ...
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
... without changing its value. In Aristotle this meant simply that the pairs he determined could be exchanged. The intuition might have been that they “essentially mean the same”. In a more abstract, and later formulation, one would say that “not to affect a proposition” is “not to change its truth val ...
... without changing its value. In Aristotle this meant simply that the pairs he determined could be exchanged. The intuition might have been that they “essentially mean the same”. In a more abstract, and later formulation, one would say that “not to affect a proposition” is “not to change its truth val ...