a-logic - Digital Commons@Wayne State University
... paradox of the liar and related paradoxes were raised later. Other problems emerged as proponents tried to apply standard logic to the empirical sciences. These included the problems of contrary-to-fact conditionals, of dispositional predicates, of confirmation theory and of probabilities for condit ...
... paradox of the liar and related paradoxes were raised later. Other problems emerged as proponents tried to apply standard logic to the empirical sciences. These included the problems of contrary-to-fact conditionals, of dispositional predicates, of confirmation theory and of probabilities for condit ...
PowerPoint
... Interpretations & models • Reasoning with ground clauses identical to reasoning with propositional clauses (treating each term like a proposition). • An interpretation is defined to be a model for a non-ground clause if it is a model for every ground instance. • So to show M = {obliged_to(compaq, fr ...
... Interpretations & models • Reasoning with ground clauses identical to reasoning with propositional clauses (treating each term like a proposition). • An interpretation is defined to be a model for a non-ground clause if it is a model for every ground instance. • So to show M = {obliged_to(compaq, fr ...
Combined unsigned and two`s complement saturating multipliers
... usefulness in these types of applications, support for saturating arithmetic has been added to several instruction set architecture extensions [1], [4], [5], [6]. Saturating arithmetic operations are also supported on most commercial digital signal processors [7]. With saturating multiplication, pro ...
... usefulness in these types of applications, support for saturating arithmetic has been added to several instruction set architecture extensions [1], [4], [5], [6]. Saturating arithmetic operations are also supported on most commercial digital signal processors [7]. With saturating multiplication, pro ...
Labeled Natural Deduction for Temporal Logics
... analysis (e.g., natural deduction, sequent systems), they have been given for specific logics and do not seem to be easily generalizable to a modular treatment of a wide range of logics of time. The aim of this thesis is to provide a modular approach to the definition of deduction systems for a larg ...
... analysis (e.g., natural deduction, sequent systems), they have been given for specific logics and do not seem to be easily generalizable to a modular treatment of a wide range of logics of time. The aim of this thesis is to provide a modular approach to the definition of deduction systems for a larg ...
Ribbon Proofs - A Proof System for the Logic of Bunched Implications
... BI is presented in [32] and elsewhere as a logic for reasoning about resource. With its two conjunctions it can contrast the notion that A and B share resources (A ∧ B) and the notion that they have disjoint resources (A ∗ B). We are particularly interested in the work of Ishtiaq, O’Hearn, Reynolds, ...
... BI is presented in [32] and elsewhere as a logic for reasoning about resource. With its two conjunctions it can contrast the notion that A and B share resources (A ∧ B) and the notion that they have disjoint resources (A ∗ B). We are particularly interested in the work of Ishtiaq, O’Hearn, Reynolds, ...
Goal-directed Proof Theory
... they are human oriented; they are a generalization of logic programming style of deduction. Goal-directed methods can be seen as an attempt to ll the gap between the two paradigms, on one hand, they maintain the perspicuity of human-oriented proof methods, on the other hand, are not too far fro ...
... they are human oriented; they are a generalization of logic programming style of deduction. Goal-directed methods can be seen as an attempt to ll the gap between the two paradigms, on one hand, they maintain the perspicuity of human-oriented proof methods, on the other hand, are not too far fro ...
Color - Alex Kocurek
... Very often, these inexpressibility claims are justified in the literature only by example: all of the most straightforward attempts at formalizing these English sentences into first-order modal logic fail. While this style of argument may be convincing, it does not constitute a proof. One can someti ...
... Very often, these inexpressibility claims are justified in the literature only by example: all of the most straightforward attempts at formalizing these English sentences into first-order modal logic fail. While this style of argument may be convincing, it does not constitute a proof. One can someti ...
JUXTAPOSITION - Brown University
... of propositional logics. The approach to semantics employed here is broadly algebraic. I consider two semantic frameworks. The first involves sets of logical matrices, algebras with an arbitrary set of designated values. The second, more interesting, framework involves sets of unital matrices, algeb ...
... of propositional logics. The approach to semantics employed here is broadly algebraic. I consider two semantic frameworks. The first involves sets of logical matrices, algebras with an arbitrary set of designated values. The second, more interesting, framework involves sets of unital matrices, algeb ...
Interpretability formalized
... Lev Beklemishev, Nick Bezhanishvili, Marta Bilkova, Marco Vervoort and Albert Visser. A special word of thanks is due to Marco Vervoort, not only for his computer support, but more important, for helping me out on the proof of the Bisimulation Lemma. Without his fundamental sequence, I would probabl ...
... Lev Beklemishev, Nick Bezhanishvili, Marta Bilkova, Marco Vervoort and Albert Visser. A special word of thanks is due to Marco Vervoort, not only for his computer support, but more important, for helping me out on the proof of the Bisimulation Lemma. Without his fundamental sequence, I would probabl ...
PhD Thesis First-Order Logic Investigation of Relativity Theory with
... method, but we can discover new, interesting and physically relevant theories. That happened in the case of the axiom of parallels in Euclid’s geometry; and this kind of investigation led to the discovery of hyperbolic geometry. Our FOL theory of accelerated observers (AccRel), which nicely fills th ...
... method, but we can discover new, interesting and physically relevant theories. That happened in the case of the axiom of parallels in Euclid’s geometry; and this kind of investigation led to the discovery of hyperbolic geometry. Our FOL theory of accelerated observers (AccRel), which nicely fills th ...
.pdf
... Many schedulers implement safety properties—they rule out certain assignments of processors to processes. Formalizations for these schedulers have much in common. Let Π be the set of processes to be executed in a system with N processors. For each process π, two pieces of information are maintained ...
... Many schedulers implement safety properties—they rule out certain assignments of processors to processes. Formalizations for these schedulers have much in common. Let Π be the set of processes to be executed in a system with N processors. For each process π, two pieces of information are maintained ...
Announcement as effort on topological spaces
... called subset space logic (SSL), in order to formalize reasoning about sets and points together in a particular modal system. The main interest in their investigation lies in spatial structures such as topological spaces, and using modal logic and the techniques behind it for spatial reasoning; howe ...
... called subset space logic (SSL), in order to formalize reasoning about sets and points together in a particular modal system. The main interest in their investigation lies in spatial structures such as topological spaces, and using modal logic and the techniques behind it for spatial reasoning; howe ...
Strong Normalisation for a Gentzen-like Cut
... We can now formally introduce sequents, or typing judgements. They are of the form Γ . M . ∆ with Γ being an antecedent, M a term and ∆ a succedent. Henceforth we shall be interested in only well-typed terms; this means those for which there are two contexts, Γ and ∆, such that Γ . M . ∆ holds given ...
... We can now formally introduce sequents, or typing judgements. They are of the form Γ . M . ∆ with Γ being an antecedent, M a term and ∆ a succedent. Henceforth we shall be interested in only well-typed terms; this means those for which there are two contexts, Γ and ∆, such that Γ . M . ∆ holds given ...
5 model theory of modal logic
... structures, the two independent directions of generalisation, and in particular the divide between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logi ...
... structures, the two independent directions of generalisation, and in particular the divide between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logi ...
How to Go Nonmonotonic Contents David Makinson
... This overview is directed to those who have heard of nonmonotonic reasoning and would like to get a better idea of what it is all about. What are its driving ideas? In what ways does it differ from classical logic? How does it relate to probability? More generally, how does it behave and how can it ...
... This overview is directed to those who have heard of nonmonotonic reasoning and would like to get a better idea of what it is all about. What are its driving ideas? In what ways does it differ from classical logic? How does it relate to probability? More generally, how does it behave and how can it ...
a semantic perspective - Institute for Logic, Language and
... triple M = (W, {Rm }m∈MOD , V ), where W , the domain, is a non-empty set (whose elements we usually call points), each Rm is a binary relation on W , and V is a function (the valuation) that assigns to each proposition symbol p in PROP a subset V (p) of W ; think of V (p) as the set of points in M ...
... triple M = (W, {Rm }m∈MOD , V ), where W , the domain, is a non-empty set (whose elements we usually call points), each Rm is a binary relation on W , and V is a function (the valuation) that assigns to each proposition symbol p in PROP a subset V (p) of W ; think of V (p) as the set of points in M ...
Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic
... structures, the two independent directions of generalisation, and in particular the divide between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. ...
... structures, the two independent directions of generalisation, and in particular the divide between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. ...
Independence logic and tuple existence atoms
... M |=X ∃xφ iff for all s ∈ X , ∃m ∈ Dom(M) s.t. M |=s[m/x] φ; M |=X ∀xφ iff for all s ∈ X , ∀m ∈ Dom(M), M |=s[m/x] φ. ...
... M |=X ∃xφ iff for all s ∈ X , ∃m ∈ Dom(M) s.t. M |=s[m/x] φ; M |=X ∀xφ iff for all s ∈ X , ∀m ∈ Dom(M), M |=s[m/x] φ. ...
On Weak Ground
... claim describes the explanatory role the weak grounds for a fact may play. Fine suggests that we may use this specification of the explanatory role that full weak grounds play to define the notion of weak ground [Fine, 2012b, p. 52]. The idea is that some facts weakly ground φ if and only if they st ...
... claim describes the explanatory role the weak grounds for a fact may play. Fine suggests that we may use this specification of the explanatory role that full weak grounds play to define the notion of weak ground [Fine, 2012b, p. 52]. The idea is that some facts weakly ground φ if and only if they st ...
SEQUENT SYSTEMS FOR MODAL LOGICS
... The philosophical (and methodological) problems with applying the notion of a Gentzen sequent to modal logics have to do with the idea of defining the logical operations by means of introduction schemata (together with structural assumptions about derivability formulated in terms of structural rules ...
... The philosophical (and methodological) problems with applying the notion of a Gentzen sequent to modal logics have to do with the idea of defining the logical operations by means of introduction schemata (together with structural assumptions about derivability formulated in terms of structural rules ...
Logic and Proof - Numeracy Workshop
... The writing and reading maths workshop covered some shorthand notation to replace common mathematical words and phrases. Here is another one: “∀” stands for “for all” or “for every possible value of”. We can use this to shorten written statements: Adding one to a number always makes the number great ...
... The writing and reading maths workshop covered some shorthand notation to replace common mathematical words and phrases. Here is another one: “∀” stands for “for all” or “for every possible value of”. We can use this to shorten written statements: Adding one to a number always makes the number great ...
1 Non-deterministic Phase Semantics and the Undecidability of
... contains a more extensive study of the semantics of the eILL fragment with completeness results for various classes of models. We did not consider models of separation logic like those of HM and SA; on the contrary, we focused on the links between BBI and linear logic. Such models of separation logi ...
... contains a more extensive study of the semantics of the eILL fragment with completeness results for various classes of models. We did not consider models of separation logic like those of HM and SA; on the contrary, we focused on the links between BBI and linear logic. Such models of separation logi ...
Self-Referential Probability
... on a supervaluational evaluation scheme. This variation is particularly interesting because it bears a close relationship to imprecise probabilities where agents’ credal states are taken to be sets of probability functions. In this chapter, we will also consider how to use this language to describe ...
... on a supervaluational evaluation scheme. This variation is particularly interesting because it bears a close relationship to imprecise probabilities where agents’ credal states are taken to be sets of probability functions. In this chapter, we will also consider how to use this language to describe ...
Ethical Intuitionism: The Meaning of Meaning Senior
... the temple of logic. In order to engage in combat with ethical intuitionists, critics must desecrate that temple2. However, it is at this point, just where intuitionism appears most formidable, where a fatal vulnerability exposes itself. Galvanized by the credibility logic confers to their system, ...
... the temple of logic. In order to engage in combat with ethical intuitionists, critics must desecrate that temple2. However, it is at this point, just where intuitionism appears most formidable, where a fatal vulnerability exposes itself. Galvanized by the credibility logic confers to their system, ...
Jesús Mosterín
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Jesús Mosterín (born 1941) is a leading Spanish philosopher and a thinker of broad spectrum, often at the frontier between science and philosophy.