81.
Remark on intuitionistic fuzzy logic and intuitionistic logic
- Atanassov, Krassimir T.
It is shown that the axioms of the intuitionistic logic can be proved as theorems in the frames of the intuitionistic fuzzy logic.
82.
Modular Temporal Logic
- Augustin Baziramwabo; Pierre Mckenzie; Denis Thérien
Thérien and Wilke characterized the Until hierarchy of linear temporal logic in terms of aperiodic monoids. Here, a temporal operator able to count modulo q is introduced. Temporal logic augmented with such operators is found decidable as it is shown to express precisely the solvable regular languages. Natural hierarchies are shown to arise when modular and conventional operators are interleaved. Modular operators are then cast as special cases of more general "group" temporal operators which, added to temporal logic, allow capturing any regular language L in much the same way that the syntactic monoid of L is constructed from groups...
83.
Linear Logic complements Classical Logic
- Vaughan Pratt
Classical logic enforces the separation of individuals and predicates, linear logic draws them
together via interaction; these are not right-or-wrong alternatives but dual or complementary
logics. Linear logic is an incomplete realization of this duality. While its completion is not
essential for the development and maintenance of logic, it is crucial for its application. We
outline the "four-square" program for completing the connection, whose corners are set, function,
number, and arithmetic, and define ordinal Set, a bicomplete equational topos, meaning its
canonical isomorphisms are identities, including associativity of product.
1 A Postcard from the Edge
Hi, boss. Just took over source's shift.
Did you hear about the line and...
84.
Monotonic and Residuated Logic Programs
- Carlos Viegas Damásio; Luís Moniz Pereira
In this paper we define the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated. Whenever defining new logic programming extensions, we can thus turn our attention to the stipulation and study of its intuitive algebraic properties within the very general setting. Then, the existence of a minimum model and of a monotonic immediate consequences operator is guaranteed, and they are related as in classical logic programming. Afterwards we study the more restricted class of residuated logic programs which is able to capture several quite distinct logic programming semantics. Namely: Generalized...
85.
Monotonic and Residuated Logic Programs
- Carlos Viegas Damásio; Luís Moniz Pereira
In this paper we define the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated. Whenever defining new logic programming extensions, we can thus turn our attention to the stipulation and study of its intuitive algebraic properties within the very general setting. Then, the existence of a minimum model and of a monotonic immediate consequences operator is guaranteed, and they are related as in classical logic programming. Afterwards we study the more restricted class of residuated logic programs which is able to capture several quite distinct logic programming semantics. Namely: Generalized...
86.
An Application of Logic
- Renata P. De Freitas; Progr Eng; Sist Comput
We consider a paradigm of applications of Logic Engineering to illustrate the information interchange among different areas of knowledge, through the formal approach to some aspects of computing. We apply the paradigm to the area of distributed systems, taking the demand for specification formalisms, treated in three areas of knowledge: modal logics, first-order logic and algebra. In doing so, we obtain transfer of intuitions and results, establishing that, as far as input/output representation is concerned, these three formalisms are equivalent.
87.
Logic Without Syntax
- Hughes, Dominic
This paper presents an abstract, mathematical formulation of classical
propositional logic. It proceeds layer by layer: (1) abstract, syntax-free
propositions; (2) abstract, syntax-free contraction-weakening proofs; (3)
distribution; (4) axioms (p OR NOT p).
Abstract propositions correspond to objects of the category G(Rel^L) where G
is the Hyland-Tan double glueing construction, Rel is the standard category of
sets and relations, and L is a set of literals.
Abstract proofs are morphisms of a tight orthogonality subcategory of
Gl(Rel^L), where we define Gl as a lax variant of G. We prove that the free
binary product-sum category (contraction-weakening logic) over L is a full
subcategory of Gl(Rel^L), and the free...
88.
FLEB: A Fuzzy Logic e-Book
- Bermúdez, Andrés; Barriga, Angel; Baturone, M.ª Iluminada; Sánchez-Solano, Santiago
FLEB is an electronic book which attempts to introduce the basic mathematical foundations and applications of fuzzy logic through a software environment which includes images, hypertext, sensitive elements, animations and interactive demos. It also allows executing Xfuzzy, a development tool which eases the description, verification, and synthesis of fuzzy logic-based systems. FLEB, like a usual book, is structured into chapters with pages through which the reader can navigate comfortably. In addition, the information provided can be accessed in a non sequential way thanks to the hypertext and sensitive elements that interconnect linked pages. This capability of non sequential reading together...
89.
Ordered Linear Logic Programming
- Frank Pfenning; Jeff Polakow; Jeff Polakow
this paper we investigate logic programming with ordered hypotheses. We follow the paradigm that logic programming should be understood via an abstract notion of uniform derivation [MNPS91] which, in a slight abuse of terminology, we take to encompass goal-directed search and focussed use of hypotheses [And92]. Somewhat unexpectedly, the extension of these notions from the case of linear logic [HM94] is far from straightforward. The principal contributions of this paper are 1. a system of ordered uniform derivations which is sound and complete with respect to OLL; 2. a model of resource consumption which removes non-determinism from resource allocation during...
90.
Between logic and probability
- Sales, Ton
Logic and Probability, as theories, have been developed quite independently and, with a few exceptions (like Boole's), have largely ignored each other. And nevertheless they share a lot of similarities, as well a considerable common ground. The exploration of the shared concepts and their mathematical treatment and unification is here attempted following the lead of illustrious researchers (Reichenbach, Carnap, Popper, Gaifman, Scott & Krauss, Fenstad, Miller, David Lewis, Stalnaker, Hintikka or Suppes, to name a few). The resulting theory, to be distinguished from the many-valued-Logics tradition, is strongly reminiscent, in its the mathematical treatment, of Probability theory, though it remains...
91.
(T, ^, N) fuzzy logic
- Xu, Y.; Liu, J.; Ruan, D.
To investigate more reasonable fuzzy reasoning model in expert systems as well as more effective logical circuit in fuzzy control, a (T, ^, N) fuzzy logic is proposed in this paper by using T-norm, ^-norm and pseudo-complement N as the logical connectives. Two aspects are discussed: (1) some concepts of (T, ^, N) fuzzy logic are introduced and some properties of (T, ^, N) fuzzy logical formulae are discussed. (2) G-fuzzy truth (falsity) of (T, ^, N) fuzzy logical formulae are investigated and also the relation between the Boolean truth (falsity) of ^-normal forms (T-normal forms) and the G-fuzzy truth...
92.
Subtractive Logic
- Tristan Crolard
This paper is the first part of a work whose purpose is to investigate duality
in some related frameworks (cartesian closed categories, lambda-calculi, intuitionistic
and classical logics) from syntactic, semantical and computational
viewpoints. We start with category theory and we show that any bicartesian
closed category with coexponents is degenerated (i.e. there is at most one
arrow between two objects). The remainder of the paper is devoted to logical
issues. We examine the propositional calculus underlying the type system of
bicartesian closed categories with coexponents and we show that this calculus
corresponds to subtractive logic: a conservative extension of intuitionistic
logic with a new connector (subtraction) dual to implication....
93.
Computing multiple-valued logic programs
- Lu, James J.; Calmet, Jacques; Schü, Joachim
The logic of signed formula can be used to reason about a wide variety of multiple-valued logics [Häh94b, LMR97]. The formal theoretical foundation of multiple-valued logic programming based on signed formulas is set forth in [Lu96]. The current paper is an investigation into the operational semantics of such signed logic programming. The connection of signed logic programming to constraint logic programming is presented, search space issues are briefly discussed for both general and special cases, and applications to bilattice logic programming and truth-maintenance are analyzed.
94.
Ordered Linear Logic Programming
- Jeff Polakow; Frank Pfenning; Frank Pfenning
this paper we investigate logic programming with ordered hypotheses. We follow the paradigm that logic programming should be understood via an abstract notion of uniform derivation [MNPS91] which, in a slight abuse of terminology, we take to encompass goal-directed search and focussed use of hypotheses [And92]. Somewhat unexpectedly, the extension of these notions from the case of linear logic [HM94] is far from straightforward. The principal contributions of this paper are 1. a system of ordered uniform derivations which is sound and complete with respect to INCLL; 2. a model of resource consumption which removes non-determinism from resource allocation during...
95.
Algebraic closure in continuous logic
- Henson, C. Ward; Tellez, Hernando
We study the algebraic closure construction for metric structures in the setting of continuous first order logic. We give several characterizations of algebraicity, and we prove basic properties analogous to ones that algebraic closure satisfies in classical first order logic.
96.
Una cadena de reforzamientos difusos de la lógica del entrañamiento
- Peña, Lorenzo
En: III Congreso español de tecnologías y lógica fuzzy
comp. por S. Barro & A. Sobrino.
Santiago de Compostela: Universidad de Santiago, 1993
pp. 115-22. ISBN 84-604-7510-7.
97.
Addendum to the paper Belnap's
- Four-valued Logic,De Morgan
three above mentioned Gentzen systems are presented, together
with the structural and multiple-conclusion versions
GBC and
GBC of GB and GBL ,
respectively. Then Theorem 4.88 of [7] states the same as Theorem 4.11 of [3], that is,
the strong algebraizability of GB (denoted by GBC in [7]), with the variety DM of De
Morgan lattices as its equivalent algebraic semantics. And Theorem 4.98 of [7] states
the non-algebraizability of
GBC , which is proved from the strong algebraizability of
GBC ; since it is obvious that the same fact and proof hold for their single-conclusion
fragments, one can consider that this result also contains the non-algebraizability
of GBL , which...
98.
Minimal logic programs
- Pedro Cabalar; David Pearce; Agustín Valverde
Abstract. bb We consider the problem of obtaining a minimal logic program strongly equivalent (under the stable models semantics) to a given arbitrary propositional theory. We propose a method consisting in the generation of the set of prime implicates of the original theory, starting from its set of countermodels (in the logic of Here-and-There), in a similar vein to the Quine-McCluskey method for minimisation of boolean functions. As a side result, we also provide several results about fundamental rules (those that are not tautologies and do not contain redundant literals) which are combined to build the minimal programs. In particular,...
99.
Locality for Classical Logic
- Bruennler, Kai
In this paper we will see deductive systems for classical propositional and
predicate logic in the calculus of structures. Like sequent systems, they have
a cut rule which is admissible. In addition, they enjoy a top-down symmetry and
some normal forms for derivations that are not available in the sequent
calculus. Identity axiom, cut, weakening and also contraction can be reduced to
atomic form. This leads to rules that are local: they do not require the
inspection of expressions of unbounded size.
100.
Combinatory Logic
- Cem Bozsahin
We describe the connections between the primitives of Combinatory
Logic and operations in natural language syntax. We also show how word
order variation in Turkish syntax can be explained by a few primitives of
Combinatory Logic. A computational framework for Turkish syntax for
parsing surface structures into combinator expressions is outlined. Evaluation
of combinator expressions (semantic forms) has been shown to be
similar to interpreting functional programming languages.
