341.
Independent Choices and the Interpretation of IF Logic
- Theo M. V. Janssen
Abstract. In this paper it is argued that Hintikka’s game theoretical semantics for Independence Friendly logic does not formalize the intuitions about independent choices; it rather is a formalization of imperfect information. Furthermore it is shown that the logic has several strange properties. An alternative semantics is proposed which formalizes intuitions about independence.
342.
Independent Choices and the Interpretation of IF Logic
- Theo M. V. Janssen
Abstract. In this paper it is argued that Hintikka’s game theoretical semantics for Independence Friendly logic does not formalize the intuitions about independent choices; it rather is a formalization of imperfect information. Furthermore it is shown that the logic has several strange properties (e.g. renaming of bound variables is not allowed). An alternative semantics is proposed which formalizes intuitions about independence.
343.
AXIOMATIZATION OF CREDULOUS REASONING IN RATIONAL DEFAULT LOGIC
- Mihaiela Lupea
Abstract. Nonmonotonic reasoning is succesfully formalized by the class of default logics. In this paper we introduce an axiomatic system for credulous reasoning in rational default logic. Based on classical sequent calculus and anti-sequent calculus, an abstract characterization of credulous nonmonotonic default inference in this variant of default logic is presented.
344.
Deontic Logic as Founded on Nonmonotonic Logic
- John F. Horty
this paper, however, that the techniques
of nonmonotonic logic may provide a better theoretical framework---at least for the formalization
of commonsense normative reasoning---than the usual modal treatment. After
reviewing some standard approaches to deontic logic, I focus on two areas in which nonmonotonic
techniques promise improved understanding: reasoning in the presence of conflicting
obligations, and reasoning with conditional obligations.
2 Modal techniques in deontic logic
345.
Deontic Logic as Founded on Nonmonotonic Logic
- John F. Horty
this paper, however, that the techniques
of nonmonotonic logic may provide a better theoretical framework---at least for the formalization
of commonsense normative reasoning---than the usual modal treatment. After
reviewing some standard approaches to deontic logic, I focus on two areas in which nonmonotonic
techniques promise improved understanding: reasoning in the presence of conflicting
obligations, and reasoning with conditional obligations.
2 Modal techniques in deontic logic
346.
Efficient Resource Management for Linear Logic Proof Search
- Iliano Cervesato; Joshua S. Hodas; Frank Pfenning
The design of linear logic programming languages and theorem provers opens a number of new implementation challenges not present in more traditional logic languages such as Horn clauses (Prolog) and hereditary Harrop formulas (Prolog and Elf ). Among these, the problem of eciently managing the linear context when solving a goal is of crucial importance for the use of these systems in non-trivial applications. This paper studies this problem in the case of Lolli [10], though its results have application to other systems including those based on linear type theory. We rst give a proof-theoretic presentation of the operational semantics...
347.
Performance Comparison between Conventional and Logic Programming Systems
- Vanusa Menditi Calegario; Inês de Castro Dutra
This work compares and analyses conventional and logic programming systems using a qualitative and quantitative approach. Logic programming is known to be easier and simpler than imperative programming, but it is not very popular because of its believed inefficiency. Our work shows that logic programming can be as efficient as imperative programming for a wide range of symbolic and scientific applications. We used different Prolog-based systems, including SICStus, XSB, Yap, CLP(R) and Aurora and compared to C, a structured language. We focus our studies on programmability, execution times and memory usage, and show that the use of techniques such as...
348.
Proving Termination of Logic Programs with Delay Declarations
- Elena Marchiori And; E. Marchiori; F. Teusink; Issn -x; Mathematisch Centrum (smc; The Dutch Foundation; Elena Marchiori; Frank Teusink
In this paper we propose a method for proving termination of logic programs with delay declarations. The method is based on the notion of recurrent logic program, which is used to prove programs terminating with respect to an arbitrary selection rule. Most importantly, we use the notion of bound query (as proposed by M. Bezem) in the definition of cover , a new notion which forms the kernel of our approach. We introduce the class of delay recurrent programs and prove that programs in this class terminate for all local delay selection rules, provided that the delay conditions imply boundedness....
349.
Infinitary Default Logic for Specification of Nonmonotonic Reasoning
- Joeri Engelfriet Wiktor; V. Wiktor Marek
. In this paper we study constructions leading to the formation of belief sets by agents. We focus on the situation when possible belief sets are built incrementally in stages. We call an infinite sequence of theories that represents such a process a reasoning trace. A set of reasoning traces describing all possible reasoning scenarios for the agent is called a reasoning frame. Default logic by Reiter is not powerful enough to represent reasoning frames. In the paper we introduce a generalization of default logic of Reiter by allowing infinite sets of justifications. We call this formalism infinitary default logic....
350.
A temporal dynamic logic for verifying hybrid system invariants
- André Platzer
Abstract. We combine first-order dynamic logic for reasoning about possible behaviour of hybrid systems with temporal logic for reasoning about the temporal behaviour during their operation. Our logic supports verification of hybrid programs with first-order definable flows and provides a uniform treatment of discrete and continuous evolution. For our combined logic, we generalise the semantics of dynamic modalities to refer to hybrid traces instead of final states. Further, we prove that this gives a conservative extension of dynamic logic. On this basis, we provide a modular verification calculus that reduces correctness of temporal behaviour of hybrid systems to non-temporal reasoning....
351.
A Deterministic Terminating Sequent Calculus for Gödel-Dummett logic
- Roy Dyckhoff; Godel-dummett Logic
We give a short proof-theoretic treatment of a terminating contraction-free calculus G4-LC for the zero-order Godel-Dummett logic LC. This calculus is a slight variant of a calculus given by Avellone et al, who show its completeness by model-theoretic techniques. In our calculus, all the rules of G4-LC are invertible, thus allowing a deterministic proof-search procedure. Keywords: sequent calculus, contraction-free, terminating, Godel-Dummett logic 1 Introduction In previous work [9] the author gave a "contraction-free calculus" for zero-order intuitionistic logic IPL; following [21] we call this calculus G4ip. It has the property that root-first proof search terminates, thus allowing easy implementation without...
352.
Homogenizing Multi-Adjoint Logic Programs
- Jesus Medina; Manuel Ojeda-Aciego
The concept of homogeneous multi-adjoint logic program is introduced, and a procedure to homogenize an arbitrary multi-adjoint logic program is presented. The procedure is proved to preserve models and, moreover, some complexity results are given.
353.
Possibilistic Logic
- Didier Dubois,Henri Prade
This paper is organized as follows : Section 2 pursues the overview by introducing background material on fuzzy set and possibility theory, including comparative possibility relations that underlie possibility and necessity measures. Section 3 forms the main body of the paper and presents formal aspects of a fragment of possibilistic logic where formulas are valued by a lower bound on their degree of necessity. It includes an axiomatization and a refutation method based on extended resolution that is liable of implementation on a computer and supports partial inconsistency. The remainder of Section 3 lays bare the existing links between possibilistic...
354.
Application of fuzzy logic in seismic zonation
- Guo, Wanwu.
Traditional statistical methods for seismic zonation require information from many subjects, such as regional geology and neotectonics, seismicity, stress field, damage analysis of historic earthquakes, geophysics and others. These subjects are weighted differently during statistics. In fact, the information from most of these subjects is more like fuzzy sets, ie, it is a sort of estimation rather than precise data. In this paper we propose a fuzzy logic system that uses crustal structural features (seismotectonics) and historic seismic activities (seismicity) as two fuzzy inputs for seismic zonation. Seismotectonics is a combination of features from regional and deep geology, neotectonics, stress...
355.
Application of fuzzy logic in seismic zonation
- Guo, Wanwu.
Traditional statistical methods for seismic zonation require information from many subjects, such as regional geology and neotectonics, seismicity, stress field, damage analysis of historic earthquakes, geophysics and others. These subjects are weighted differently during statistics. In fact, the information from most of these subjects is more like fuzzy sets, ie, it is a sort of estimation rather than precise data. In this paper we propose a fuzzy logic system that uses crustal structural features (seismotectonics) and historic seismic activities (seismicity) as two fuzzy inputs for seismic zonation. Seismotectonics is a combination of features from regional and deep geology, neotectonics, stress...
356.
Yet another decision procedure for equality logic
- Orly Meir; Ofer Strichman
Abstract. We introduce a new decision procedure for Equality Logic. The procedure improves on Bryant and Velev’s sparse method [4] from CAV’00, in which each equality predicate is encoded with a Boolean variable, and then a set of transitivity constraints are added to compensate for the loss of transitivity of equality. We suggest the Reduced Transitivity Constraints (rtc) algorithm, that unlike the sparse method, considers the polarity of each equality predicate, i.e. whether it is an equality or disequality when the given equality formula ϕ E is in Negation Normal Form (NNF). Given this information, we build the Equality Graph...
357.
First Order Logic
er logic can still be adequate programming languages.
Mathematicians have used first order logic as a programming language
in which to encode all the known acceptable principles of mathematical
inference. The result is axiomatic set theory. Any mathematical proof can,
in principle, be expressed as a proof in first order set theory. In this sense
axiomatic set theory is an adequate foundation for mathematics. However,
it is known that these principles of inference are not complete, e.g., there are
true statements about integers which can not be proven. This implies that
there are true statements that can never be proven by mathematicians (unless
new principles are adopted). It is...
358.
First Order Logic
st order logic can still be adequate programming languages.
Mathematicians have used first order logic as a programming language
in which to encode all the known acceptable principles of mathematical
inference. The result is axiomatic set theory. Any mathematical proof can,
in principle, be expressed as a proof in first order set theory. In this sense
axiomatic set theory is an adequate foundation for mathematics. However,
it is known that these principles of inference are not complete, e.g., there are
true statements about integers which can not be proven. This implies that
there are true statements that can never be proven by mathematicians (unless
new principles are adopted). It...
359.
Computational Logic in Australia
interpretation is a language-independent
theory for static analysis of programs. This theory
plays a prominent role in much work in the group,
since most sophisticated implementation ideas require
static analysis. The work contributes to the theory
generally, as well as its applications in functional and
logic programming, including sophisticated program
transformation.
Techniques are also being developed to dramatically
reduce the time and effort spent on debugging.
Traditional debugging techniques are based on following
the steps of program execution. With high-level
languages such as logic programming languages, the
sequence of execution steps can be very complex.
Declarative debugging is an interactive technique
that pinpoints errors using programmers' responses to
queries. The program, as a logical description of...
360.
First Order Logic
first order logic can still be adequate programming languages.
Mathematicians have used first order logic as a programming language
in which to encode all the known acceptable principles of mathematical
inference. The result is axiomatic set theory. Any mathematical proof can,
in principle, be expressed as a proof in first order set theory. In this sense
axiomatic set theory is an adequate foundation for mathematics. However,
1
it is known that these principles of inference are not complete, e.g., there are
true statements about integers which can not be proven. This implies that
there are true statements that can never be proven by mathematicians (unless
new principles are adopted). It...
