101.
A Judgmental Analysis of Linear Logic
- Bor-Yuh Evan Chang; Kaustuv Chaudhuri; Frank Pfenning
We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva's full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in...
102.
A Judgmental Analysis of Linear Logic
- Bor-Yuh Evan Chang; Chang Kaustuv; Chaudhuri Frank Pfenning
We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva's full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in...
103.
A Judgmental Analysis of Linear Logic
- Bor-Yuh Evan Chang; Kaustuv Chaudhuri; Frank Pfenning
We reexamine the foundations of linear logic, developing a system of natural deduction following Martin-L of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva's full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in...
104.
Quantum logic as motivated by quantum computing
- Dunn, J. Michael; Hagge, Tobias J.; Moss, Lawrence S.; Wang, Zhenghan
We explore a connection between quantum logic and quantum computing.
105.
A Judgmental Analysis of Linear Logic
- Bor-Yuh Evan Chang; Chang Kaustuv; Chaudhuri Frank Pfenning
We reexamine the foundations of linear logic, developing a system of natural deduction following Martin-L of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva's full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in...
106.
Classical Logic = Fibred MLL
- Hughes, Dominic
This paper represents classical propositional proofs as *combinatorial
proofs*, which are more abstract than proof nets: superposition
(contraction/weakening) is modelled mathematically, as a lax form of fibration,
rather than syntactically (as in proof nets, which involve contraction and
weakening nodes). A combinatorial proof is a `fibred' multiplicative linear
proof net, hence the slogan in the title. Cut elimination retains its richness
from sequent calculus: its non-determinism does not collapse to become
confluent. [Note: this is merely a 2-page synopsis, accepted for a short
presentation at Logic in Computer Science '05.]
107.
Temporal Logic
- Yde Venema
this paper, section 3, is
devoted to a fairly detailed exposition of Prior's basic tense logic; the aim of this is not only
to introduce the readers to this particular system, but perhaps even more to acquaint them
with the kind of questions that temporal logicians tend to ask. In the sections 4 and 5 we
present some extensions and alternatives to this base system. In section 6 we sketch some
developments that have taken place over the last ten years or so. Finally, in the epilogue we
try to answer the question what Temporal Logic is; this section also contains a short list of
monographs surveying...
108.
Temporal Logic
- Yde Venema
this paper, section 3, is
devoted to a fairly detailed exposition of Prior's basic tense logic; the aim of this is not only
to introduce the readers to this particular system, but perhaps even more to acquaint them
with the kind of questions that temporal logicians tend to ask. In the sections 4 and 5 we
present some extensions and alternatives to this base system. In section 6 we sketch some
developments that have taken place over the last ten years or so. Finally, in the epilogue we
try to answer the question what Temporal Logic is; this section also contains a short list of
monographs surveying...
109.
Logic Programs as Compact Denotations
- Patricia M. Hill; Fausto Spoto
This paper shows how logic programs can be used to implement the transition functions of denotational abstract interpretation. The logic variables express regularity in the abstract behaviour of commands. The technique has been applied to sign, class and escape analysis for object-oriented programs. We show that the time and space costs using logic programs for these analyses are smaller than those using a ground relational representation.
110.
Defeasible Logic versus Logic Programming without Negation as Failure
- Antoniou Maher And; G. Antoniou; M. J. Maher; D. Billington
Recently there has been increased interest in logic programming-based default reasoning approaches which are not using negation-as-failure in their object language. Instead, default reasoning is modelled by rules and a priority relation among them. In this paper we compare the expressive power of two approaches in this family of logics: Defeasible Logic, and sceptical LPwNF. Our results show that the former has a strictly stronger expressive power. The difference is caused by the latter logic's failure to capture the idea of teams of rules supporting a specific conclusion. Keywords: defeasible logic, logic programming without negation as failure, nonmonotonic reasoning, expressive...
111.
Design of a digital logic analyzer
- Vorhis, Gregory J.
Design of a digital logic analyzer
112.
The limits of fuzzy logic
- Castro, J. L.
In this paper we try to answer the following questions: What can be made by applying fuzzy logic? and What can not be made by applying fuzzy logic? The question will be analyzed from both a theoretical and an applied point of view. A (partial) answer will be given for three topics: a) as calculus procedure b) as reasoning mechanism and c) as engineering tool.
113.
Modelling Digital Logic in SDL
- Tadanori Mizuno; Norio Shiratori; Teruo Higashino; G. Csopaki A; K. J. Turner B
The specification of digital logic in SDL (Specification and Description Language) is investigated. A specification approach is proposed for multi-level descriptions of hardware behaviour and structure. The modelling method exploits features introduced in SDL-92. The approach also deals with the specification, analysis and simulation of timing aspects at any level in the specification of digital logic.
114.
Hoare Logic and Auxiliary Variables
- Thomas Kleymann
Auxiliary variables are essential for specifying programs in Hoare Logic. They are required to relate the value of variables in different states. However, the axioms and rules of Hoare Logic turn a blind eye to the rle of auxiliary variables. We stipulate a new structural rule for adjusting auxiliary variables when strengthening preconditions and weakening postconditions. Courtesy of this new rule, Hoare Logic is adaptation complete, which benefits software re-use. This property is responsible for a number of improvements. Relative completeness follows uniformly from the Most General Formula property. Moreover, contrary to common belief, one can show that Hoare Logic...
115.
A judgmental analysis of linear logic
- Bor-yuh Evan; Chang Kaustuv; Chaudhuri Frank Pfenning
We reexamine the foundations of linear logic, developing a system of natural deduction following Martin-Löf’s separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva’s full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in our...
116.
Hoare logic and auxiliary variables
- Thomas Kleymann
Abstract: Auxiliary variables are essential for specifying programs in Hoare Logic. They are required to relate the value of variables in different states. However, the axioms and rules of Hoare Logic turn a blind eye to the rôle of auxiliary variables. We stipulate a new structural rule for adjusting auxiliary variables when strengthening preconditions and weakening postconditions. Courtesy of this new rule, Hoare Logic is adaptation complete, which benefits software re-use. This property is responsible for a number of improvements. Relative completeness follows uniformly from the Most General Formula property. Moreover, contrary to common belief, one can show that Hoare...
117.
A Judgmental Analysis of Linear Logic
- Bor-yuh Evan; Chang Kaustuv; Chaudhuri Frank Pfenning
We reexamine the foundations of linear logic, developing a system of natural deduction following Martin-Löf’s separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva’s full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in our...
118.
Automaton Logic
- M. Schaller,K. Svozil
The experimental logic of Moore and Mealy type automata is investigated.
key words: automaton logic; partition logic; comparison to quantum logic;
intrinsic measurements
1
119.
Mapping Tile Logic into Rewriting Logic
.
1 Introduction
Mapping Tile Logic into Rewriting Logic
meseguer@csl.sri.com
ugo@di.unipi.it
Jos'e Meseguer and Ugo Montanari
Rewriting logic [27, 28, 31] extends to concurrent systems with state changes the
body of theory developed within the algebraic semantics approach. It can also be
Rewriting logic
Tile logic
membership equational logic
2
double
2VH-categories
internal strategies
uniform
Metodi e Strumenti per la Progettazione e la
Verifica di Sistemi Eterogenei Connessi mediante Reti di Comunicazione
CONFER2 COORDINA
Computer Science Laboratory, SRI International, Menlo Park,
Dipartimento di Informatica, Universit`a di Pisa,
extends to concurrent systems with state
changes the body of theory developed within the algebraic semantics approach.
It is both a foundational tool and the kernel language of several
implementation efforts (Cafe, ELAN, Maude). extends (unconditional)
rewriting logic...
120.
Logic Languages
- Andres Pozo-prieto; Juan Jose Moreno-navarro
Abstract: The paper describes the implementation of a parallel graph narrowing machine. The machine implements a functional logic language on a shared memory multiprocessor. The model of parallelism uses an independence condition to decide which subexpressions of an expression can run in parallel. The outer expression continues its execution and the synchronization with a subtask is only performed when its result is needed. The machine is fully implemented and some experimental results are shown.
