Higher Order Logic - Theory and Logic Group
... are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foun ...
... are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foun ...
Modal Consequence Relations
... from σ0 ; σ1 ; · · · ; σn−1 to δ is logically correct if whenever σi is true for all i < n, then so is δ. In place of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is valid. This approach culminated in the notion of a consequence relation, which is a relation betwee ...
... from σ0 ; σ1 ; · · · ; σn−1 to δ is logically correct if whenever σi is true for all i < n, then so is δ. In place of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is valid. This approach culminated in the notion of a consequence relation, which is a relation betwee ...
High Level Verification of Control Intensive Systems
... checking hardware/software systems. However, for control intensive systems, existing predicate abstraction techniques can potentially result in a blowup of the size of the abstract model. We deal with this problem by retaining important control variables in the abstract model. By this method we avoi ...
... checking hardware/software systems. However, for control intensive systems, existing predicate abstraction techniques can potentially result in a blowup of the size of the abstract model. We deal with this problem by retaining important control variables in the abstract model. By this method we avoi ...
Constraint propagation
... There exists a reasoning technique, such that for any theory T and formula F, such that T |= F, the reasoning technique proves T |= F. ...
... There exists a reasoning technique, such that for any theory T and formula F, such that T |= F, the reasoning technique proves T |= F. ...
Accepted for publication in the Journal of Semantics, pre
... reciprocal sentences; in addition to the features mentioned above, Chicheŵa and English reciprocals also have in common that they give rise to scope ambiguities when embedded. Dalrymple et al. (1994) concluded that the best way to deal with this semantic uniformity in the face of morphosyntactic di ...
... reciprocal sentences; in addition to the features mentioned above, Chicheŵa and English reciprocals also have in common that they give rise to scope ambiguities when embedded. Dalrymple et al. (1994) concluded that the best way to deal with this semantic uniformity in the face of morphosyntactic di ...
Views: Compositional Reasoning for Concurrent Programs
... of variables agree with their types, and the rights to change the state such that this typing is preserved. When views are composed, they must agree on the types of all variables they share. In a type system that permits strong (i.e. type-changing) updates, threads again have knowledge that variable ...
... of variables agree with their types, and the rights to change the state such that this typing is preserved. When views are composed, they must agree on the types of all variables they share. In a type system that permits strong (i.e. type-changing) updates, threads again have knowledge that variable ...
Topological aspects of real-valued logic
... Keisler is that the latter used traditional structures with a distinguished equality relation, while the former considers structures without equality, but instead equipped with a distinguished metric. More precisely, the semantic objects for continuous first-order logic are metric structures, that i ...
... Keisler is that the latter used traditional structures with a distinguished equality relation, while the former considers structures without equality, but instead equipped with a distinguished metric. More precisely, the semantic objects for continuous first-order logic are metric structures, that i ...
Proof analysis beyond geometric theories: from rule systems to
... axiomatizations does not originate from geometry but from category theory, geometric theories and their proof-theoretic treatment through the geometric rule scheme have been employed for a formalization of Euclidean geometry in Avigad et al. (2009) and for projective and affine geometry in Negri and ...
... axiomatizations does not originate from geometry but from category theory, geometric theories and their proof-theoretic treatment through the geometric rule scheme have been employed for a formalization of Euclidean geometry in Avigad et al. (2009) and for projective and affine geometry in Negri and ...
There is more than one language
... All linguistic theories agree that the phonologically interpreted expressions of a language present a fairly rich phrase structure (though just how rich varies among theories). Linguistically important relations between expressions are often characterizable directly in terms of that phrase structure ...
... All linguistic theories agree that the phonologically interpreted expressions of a language present a fairly rich phrase structure (though just how rich varies among theories). Linguistically important relations between expressions are often characterizable directly in terms of that phrase structure ...
Fichte`s Legacy in Logic
... Wissenschaftslehre” (SW I, 91ff). Some are symbolic (‘I = I’, ‘I ≠ ~I’); others discursive (‘the I is posited absolutely’, ‘I am I’). The first two principles – the principles of self-positing and counter-positing respectively – are meant to express constitutive acts (or ‘fact-acts’ – Thathandlunge ...
... Wissenschaftslehre” (SW I, 91ff). Some are symbolic (‘I = I’, ‘I ≠ ~I’); others discursive (‘the I is posited absolutely’, ‘I am I’). The first two principles – the principles of self-positing and counter-positing respectively – are meant to express constitutive acts (or ‘fact-acts’ – Thathandlunge ...
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 ...
Horn Belief Contraction: Remainders, Envelopes and Complexity
... and Hansson 2011; Hansson 1999; Peppas 2008). The standard approach, called the AGM approach after (Alchourrón, Gärdenfors, and Makinson 1985), is to formulate postulates that need to be satisfied by rational agents performing belief revision, and then to characterize all possible operations that ...
... and Hansson 2011; Hansson 1999; Peppas 2008). The standard approach, called the AGM approach after (Alchourrón, Gärdenfors, and Makinson 1985), is to formulate postulates that need to be satisfied by rational agents performing belief revision, and then to characterize all possible operations that ...
Relevant and Substructural Logics
... these sections I will endeavour to sketch the core historical lines of development in substructural logics. This, then, will be a conceptual history, indicating the linkages, dependencies and development of the content itself. I will be less concerned with identifying who did what and when.3 I take ...
... these sections I will endeavour to sketch the core historical lines of development in substructural logics. This, then, will be a conceptual history, indicating the linkages, dependencies and development of the content itself. I will be less concerned with identifying who did what and when.3 I take ...
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... premises and the conclusion. In logic, the word valid is only applied to arguments; therefore, when the concept of validity is discussed in this text, it is solely in reference to arguments, and not to claims, points, or positions. Those expressions may have other uses in other fields, but in logic, ...
... premises and the conclusion. In logic, the word valid is only applied to arguments; therefore, when the concept of validity is discussed in this text, it is solely in reference to arguments, and not to claims, points, or positions. Those expressions may have other uses in other fields, but in logic, ...
? A Unified Semantic Framework for Fully
... weakening rules, (W ⇒) and (⇒ W ), are all included. We denote by ΥG all other rules of a basic system G, and by ΠG the set of context-relations appearing in the basic rules of G (in particular, since (cut) is always included, π0 ∈ ΠG for every basic system G). Definition 3.5. A proof in a basic sys ...
... weakening rules, (W ⇒) and (⇒ W ), are all included. We denote by ΥG all other rules of a basic system G, and by ΠG the set of context-relations appearing in the basic rules of G (in particular, since (cut) is always included, π0 ∈ ΠG for every basic system G). Definition 3.5. A proof in a basic sys ...
Recursive Predicates And Quantifiers
... the relationship of the results stands out more clearly than before. The general theorem asserts that to each of an enumeration of predicate forms, there is a predicate not expressible in that form. The predicates considered belong to elementary number theory. The possibility that this theorem may a ...
... the relationship of the results stands out more clearly than before. The general theorem asserts that to each of an enumeration of predicate forms, there is a predicate not expressible in that form. The predicates considered belong to elementary number theory. The possibility that this theorem may a ...
A Logical Framework for Default Reasoning
... ∆ is a set of formulae, called the set of possible hypotheses. Any ground instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a clos ...
... ∆ is a set of formulae, called the set of possible hypotheses. Any ground instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a clos ...
Informal Proceedings of the 30th International Workshop on
... A rule A/B is passive L if its premise A is not uni able in L. Passive rules are admissible in every logic. A logic L is Almost Structurally Complete, ASC, if every admissible rule in L which is not passive is derivable (e.g. all extensions S4.3 are ASC). Projective uni cation implies ASC (or SC). L ...
... A rule A/B is passive L if its premise A is not uni able in L. Passive rules are admissible in every logic. A logic L is Almost Structurally Complete, ASC, if every admissible rule in L which is not passive is derivable (e.g. all extensions S4.3 are ASC). Projective uni cation implies ASC (or SC). L ...
