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 ...
Consequence relations and admissible rules
... Several observations in Section 3 also occur in one way or another in the book on multiple–conclusion logic by Shoesmith and Smiley [16]. But as our approach differs in some respects from the one in that book, we have included proofs also of the theorems covered there. Metcalfe in [10] studies simil ...
... Several observations in Section 3 also occur in one way or another in the book on multiple–conclusion logic by Shoesmith and Smiley [16]. But as our approach differs in some respects from the one in that book, we have included proofs also of the theorems covered there. Metcalfe in [10] studies simil ...
On perturbations of continuous structures - HAL
... A second motivation comes from some open problems concerning automorphism group of the separable model of an ω-categorical continuous theory. Such problems could be addressed from a model-theoretic point of view as questions concerning the theory TA (i.e., T with a generic automorphism, or even seve ...
... A second motivation comes from some open problems concerning automorphism group of the separable model of an ω-categorical continuous theory. Such problems could be addressed from a model-theoretic point of view as questions concerning the theory TA (i.e., T with a generic automorphism, or even seve ...
Classical Propositional Logic
... A Henkin-style Completeness Proof for Natural Deduction Computability ...
... A Henkin-style Completeness Proof for Natural Deduction Computability ...
Full abstraction for PCF - Department of Computer Science, Oxford
... abstract model is a finite poset. A natural question is whether these finite posets can be effectively presented. Suppose that we have a category of sequential domains as described in the previous paragraph, yielding a fully abstract model of PCF. If the “intensional structure” part of the interpret ...
... abstract model is a finite poset. A natural question is whether these finite posets can be effectively presented. Suppose that we have a category of sequential domains as described in the previous paragraph, yielding a fully abstract model of PCF. If the “intensional structure” part of the interpret ...
ON PERTURBATIONS OF CONTINUOUS STRUCTURES
... A second motivation comes from some open problems concerning automorphism group of the separable model of an ω-categorical continuous theory. Such problems could be addressed from a model-theoretic point of view as questions concerning the theory TA (i.e., T with a generic automorphism, or even seve ...
... A second motivation comes from some open problems concerning automorphism group of the separable model of an ω-categorical continuous theory. Such problems could be addressed from a model-theoretic point of view as questions concerning the theory TA (i.e., T with a generic automorphism, or even seve ...
Making Abstract Domains Condensing
... The main result. In general, condensing is a property of an abstract semantics S with respect to an operation ⊗, stating that for any pair of abstract objects a and b, the semantics S(a ⊗ b) can be retrieved as a ⊗ S(b). This generalizes and exactly captures the above notion of condensation when ⊗ i ...
... The main result. In general, condensing is a property of an abstract semantics S with respect to an operation ⊗, stating that for any pair of abstract objects a and b, the semantics S(a ⊗ b) can be retrieved as a ⊗ S(b). This generalizes and exactly captures the above notion of condensation when ⊗ i ...
Proof Theory for Propositional Logic
... above) is false. Again, let’s just get comfortable doing the proofs for now. When we do truth tables we will discuss why this is the case for propositional logic. In both cases, the problem reveals fundamental limitations of the logic, though more severe in the case of the conditional. At this point ...
... above) is false. Again, let’s just get comfortable doing the proofs for now. When we do truth tables we will discuss why this is the case for propositional logic. In both cases, the problem reveals fundamental limitations of the logic, though more severe in the case of the conditional. At this point ...
Logic and Proof
... Although the patterns of language addressed by Aristotle’s theory of reasoning are limited, we have him to thank for a crucial insight: we can classify valid patterns of inference by their logical form, while abstracting away specific content. It is this fundamental observation that underlies the en ...
... Although the patterns of language addressed by Aristotle’s theory of reasoning are limited, we have him to thank for a crucial insight: we can classify valid patterns of inference by their logical form, while abstracting away specific content. It is this fundamental observation that underlies the en ...
Harmony, Normality and Stability
... introduced by an application of an introduction rule and is major premise of an application of an elimination rule. Dummett calls the context in which a maximal formula occurs in a deduction a local peak, and thus harmony obtains if local peaks can be removed from deductions. Thus the requirement o ...
... introduced by an application of an introduction rule and is major premise of an application of an elimination rule. Dummett calls the context in which a maximal formula occurs in a deduction a local peak, and thus harmony obtains if local peaks can be removed from deductions. Thus the requirement o ...
AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY
... Montague now asks the same question as Kanger: How can this definition of the truthrelation ‚ be generalized to first-order languages with modal operators? As we recall, Kanger solved the problem by modifying the notion of an interpretation: a Kanger-type interpretation (what he called ‘a system’) a ...
... Montague now asks the same question as Kanger: How can this definition of the truthrelation ‚ be generalized to first-order languages with modal operators? As we recall, Kanger solved the problem by modifying the notion of an interpretation: a Kanger-type interpretation (what he called ‘a system’) a ...
Coding a Lisp Interpreter in Shen: a Case Study
... comparable to the vague intuitive notion of computability that existed prior to Turing's [23] definition of computability in 1936. We cannot prove formally that Turing's account of computability meets our intuitive concept because formal proof begins only when our intuitions have been given shape. H ...
... comparable to the vague intuitive notion of computability that existed prior to Turing's [23] definition of computability in 1936. We cannot prove formally that Turing's account of computability meets our intuitive concept because formal proof begins only when our intuitions have been given shape. H ...
A Brief Introduction to Functional Reactive Programming and Yampa
... Programming with signal functions In Yampa, systems are described by combining signal functions (forming new signal functions). For example, serial composition: ...
... Programming with signal functions In Yampa, systems are described by combining signal functions (forming new signal functions). For example, serial composition: ...
Dedukti
... quantifiers ∀ and ∃. For instance, it is not possible to define, in predicate logic, a unary function symbol 7→ that would bind a variable in its argument. 2. Predicate logic ignores the propositions-as-types principle, according to which a proof π of a proposition A is a term of type A. 3. Predicat ...
... quantifiers ∀ and ∃. For instance, it is not possible to define, in predicate logic, a unary function symbol 7→ that would bind a variable in its argument. 2. Predicate logic ignores the propositions-as-types principle, according to which a proof π of a proposition A is a term of type A. 3. Predicat ...
... There is a sense in which both validity inference and truth inference give us no more information about a logic than that which is already contained in the set of valid formulas of a logic. Thus, a validity inference (T t-, cp is sound iff, for every substitution T, either T[O] is not valid or ~ [ c ...
REGULAR COST FUNCTIONS, PART I: LOGIC AND ALGEBRA
... Leung for distance automata. This work closes the story of the star-height problem itself. The star-height problem is the king among the problems solved using this method. But there are many other (difficult) questions that can be reduced to the limitedness of distance automata and variants. Some of ...
... Leung for distance automata. This work closes the story of the star-height problem itself. The star-height problem is the king among the problems solved using this method. But there are many other (difficult) questions that can be reduced to the limitedness of distance automata and variants. Some of ...
Understanding SPKI/SDSI Using First-Order Logic
... lines. Li et al. [26] use the same idea to provide a semantics for RT0 , which can be viewed as SDSI enhanced with the intersection operator in the subject. The following presentation of the set-theoretic semantics follows [26], with ℘(K) the power set of K. If f, g : NL → ℘(K) are two functions map ...
... lines. Li et al. [26] use the same idea to provide a semantics for RT0 , which can be viewed as SDSI enhanced with the intersection operator in the subject. The following presentation of the set-theoretic semantics follows [26], with ℘(K) the power set of K. If f, g : NL → ℘(K) are two functions map ...
? A Unified Semantic Framework for Fully
... (generalized) Kripke valuations for which it is strongly sound and complete. In fact, we provide a uniform method to obtain these sets of Kripke valuations. In many important cases, the usual well-known soundness and completeness theorems for known calculi are simple corollaries of this general meth ...
... (generalized) Kripke valuations for which it is strongly sound and complete. In fact, we provide a uniform method to obtain these sets of Kripke valuations. In many important cases, the usual well-known soundness and completeness theorems for known calculi are simple corollaries of this general meth ...
Conditional XPath
... formula. More precisely, each node wff is equivalent to an F Otree formula in one free variable, and each path wff to an F Otree formula in two free variables. But not only there is a bound on the number of free variables in the corresponding first order formula, we can also bound the total number o ...
... formula. More precisely, each node wff is equivalent to an F Otree formula in one free variable, and each path wff to an F Otree formula in two free variables. But not only there is a bound on the number of free variables in the corresponding first order formula, we can also bound the total number o ...
relevance logic - Consequently.org
... on this program. By way of minor recompense we mention that Anderson and Belnap [1975] have been good about discussing related approaches, especially the older ones. Finally, we should say that our paradigm of a relevance logic throughout this essay will be the Anderson–Belnap system R or relevant i ...
... on this program. By way of minor recompense we mention that Anderson and Belnap [1975] have been good about discussing related approaches, especially the older ones. Finally, we should say that our paradigm of a relevance logic throughout this essay will be the Anderson–Belnap system R or relevant i ...
tbmk5ictk6
... We also saw two examples of invalid arguments. Both of those are unsound simply because they are invalid. Sound arguments have to be valid and have all true premises. Notice that since only arguments can be valid, only arguments can be sound. In logic, the concept of soundness is not applied to prin ...
... We also saw two examples of invalid arguments. Both of those are unsound simply because they are invalid. Sound arguments have to be valid and have all true premises. Notice that since only arguments can be valid, only arguments can be sound. In logic, the concept of soundness is not applied to prin ...
an extension of spass deciding first
... SPASS is an automated theorem prover for first-order logic which tries to proof the satisfiability or unsatisfiability of a problem. The project presented in this dissertation is to extend SPASS and to make it solve more problems than it does already. The way to achieve this aim is to make SPASS rec ...
... SPASS is an automated theorem prover for first-order logic which tries to proof the satisfiability or unsatisfiability of a problem. The project presented in this dissertation is to extend SPASS and to make it solve more problems than it does already. The way to achieve this aim is to make SPASS rec ...
User`s Functions in Standard Prolog
... significant amount of additional run-time checks even if functional expressions are not used in them. In PLN 5 [13] all these problematic concepts are replaced by the author’s simple notion of pln goals: Just two new built-in predicates, ’?’/1 (sect. 1) and constructor/2 (sect. 3) are introduced (an ...
... significant amount of additional run-time checks even if functional expressions are not used in them. In PLN 5 [13] all these problematic concepts are replaced by the author’s simple notion of pln goals: Just two new built-in predicates, ’?’/1 (sect. 1) and constructor/2 (sect. 3) are introduced (an ...
thèse - IRIT
... In the beginning of the 90s, Gelfond has introduced epistemic specifications (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Rela ...
... In the beginning of the 90s, Gelfond has introduced epistemic specifications (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Rela ...