scholarly journals Here and There with Arithmetic

2021 ◽  
pp. 1-15
Author(s):  
VLADIMIR LIFSCHITZ
Keyword(s):  
Programming Language ◽  
Propositional Logic ◽  
Answer Set Programming ◽  
The Other ◽  
Arithmetic Operations ◽  
First Order ◽  
The Relationship ◽  
Answer Set

Abstarct In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of here-and-there allows us to establish strong equivalence by deriving rules of each group from rules of the other. In the process, rules are rewritten as propositional formulas. We extend this method of proving strong equivalence to an answer set programming language that includes operations on integers. The formula representing a rule in this language is a first-order formula that may contain comparison symbols among its predicate constants, and symbols for arithmetic operations among its function constants. The paper is under consideration for acceptance in TPLP.

scholarly journals Grounding and Solving in Answer Set Programming

AI Magazine ◽  
2016 ◽  
Vol 37 (3) ◽  
pp. 25-32 ◽  
Author(s):  
Benjamin Kaufmann ◽  
Nicola Leone ◽  
Simona Perri ◽  
Torsten Schaub
Keyword(s):  
Problem Solving ◽  
Propositional Logic ◽  
Logic Program ◽  
Answer Set Programming ◽  
Key Issues ◽  
Answer Sets ◽  
Answer Set

Answer set programming is a declarative problem solving paradigm that rests upon a workflow involving modeling, grounding, and solving. While the former is described by Gebser and Schaub (2016), we focus here on key issues in grounding, or how to systematically replace object variables by ground terms in a effective way, and solving, or how to compute the answer sets of a propositional logic program obtained by grounding.

scholarly journals An ASP Approach to Generate Minimal Countermodels in Intuitionistic Propositional Logic

2019 ◽  
Author(s):  
Camillo Fiorentini
Keyword(s):  
Propositional Logic ◽  
Answer Set Programming ◽  
Kripke Model ◽  
Kripke Semantics ◽  
Minimal Models ◽  
Intuitionistic Propositional Logic ◽  
Answer Set

Intuitionistic Propositional Logic is complete w.r.t. Kripke semantics: if a formula is not intuitionistically valid, then there exists a finite Kripke model falsifying it. The problem of obtaining concise models has been scarcely investigated in the literature. We present a procedure to generate minimal models in the number of worlds relying on Answer Set Programming (ASP).

Thermodynamics of Aluminum Deoxidization Equilibria in GCr18Mo Bearing-Steel

2018 ◽  
Vol 382 ◽  
pp. 80-85 ◽  
Author(s):  
Xin Su ◽  
Shu Qiang Guo ◽  
Meng Ran Qiao ◽  
Hong Yan Zheng ◽  
Li Bin Qin
Keyword(s):  
Bearing Steel ◽  
Second Order ◽  
The Other ◽  
Interaction Parameters ◽  
Interaction Coefficients ◽  
Concentration Region ◽  
Order Interaction ◽  
First Order ◽  
The Relationship ◽  
Reaction Equilibrium

Based on the predecessors of thermodynamic data, the relationship between aluminum contents and oxygen contents of the aluminum deoxidization reaction was calculated. And the influence of activity coefficient to the reaction equilibrium in bearing-steel is analyzed. First-order and second-order interaction coefficients were used to calculate and draw the equilibrium curves, respectively. The effects of different temperature and different interaction parameters on the deoxidization equilibrium curves were studied. And through the curve the influence of the change of aluminum contents to the activity can be known. The trend of the curve with first-order interaction parameters is consistent with the curve with first-order and second-order interaction parameters at the low Al concentration region. And the oxygen contents of curve with first-order interaction parameters are higher than the other curve at the high Al concentration region

scholarly journals Recursive enumerability and elementary frame definability in predicate modal logic

2019 ◽  
Vol 30 (2) ◽  
pp. 549-560 ◽  
Author(s):  
Mikhail Rybakov ◽  
Dmitry Shkatov
Keyword(s):  
Modal Logic ◽  
Modal Logics ◽  
The Other ◽  
Kripke Semantics ◽  
First Order ◽  
Elementary Class ◽  
Recursive Enumerability ◽  
Kripke Frames ◽  
Recursively Enumerable ◽  
The Relationship

Abstract We investigate the relationship between recursive enumerability and elementary frame definability in first-order predicate modal logic. On one hand, it is well known that every first-order predicate modal logic complete with respect to an elementary class of Kripke frames, i.e. a class of frames definable by a classical first-order formula, is recursively enumerable. On the other, numerous examples are known of predicate modal logics, based on ‘natural’ propositional modal logics with essentially second-order Kripke semantics, that are either not recursively enumerable or Kripke incomplete. This raises the question of whether every Kripke complete, recursively enumerable predicate modal logic can be characterized by an elementary class of Kripke frames. We answer this question in the negative, by constructing a normal predicate modal logic which is Kripke complete, recursively enumerable, but not complete with respect to an elementary class of frames. We also present an example of a normal predicate modal logic that is recursively enumerable, Kripke complete, and not complete with respect to an elementary class of rooted frames, but is complete with respect to an elementary class of frames that are not rooted.

scholarly journals Proving infinitary formulas

2016 ◽  
Vol 16 (5-6) ◽  
pp. 787-799 ◽  
Author(s):  
AMELIA HARRISON ◽  
VLADIMIR LIFSCHITZ ◽  
JULIAN MICHAEL
Keyword(s):  
Propositional Logic ◽  
Formal System ◽  
Answer Set Programming ◽  
Logic Programs ◽  
Deductive Systems ◽  
Answer Set

AbstractThe infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic exists, but a proof in that system may include infinitely many formulas. In this note we describe a relationship between the validity of infinitary formulas in the logic of here-and-there and the provability of formulas in some finite deductive systems. This relationship allows us to use finite proofs to justify the validity of infinitary formulas.

What is an inference rule?

1992 ◽  
Vol 57 (3) ◽  
pp. 1018-1045 ◽  
Author(s):  
Ronald Fagin ◽  
Joseph Y. Halpern ◽  
Moshe Y. Vardi
Keyword(s):  
Propositional Logic ◽  
General Framework ◽  
Inference Rule ◽  
Order Logic ◽  
Classical Propositional Logic ◽  
Semantic Framework ◽  
First Order ◽  
Extremal Points ◽  
The Relationship ◽  
General Semantic

AbstractWhat is an inference rule? This question does not have a unique answer. One usually finds two distinct standard answers in the literature; validity inference (σ ⊦vφ for every substitution τ, the validity of τ[σ] entails the validity of τ[φ]), and truth inference (σ⊦l φ if for every substitution τ, the truth of τ[σ] entails the truth of τ[φ]). In this paper we introduce a general semantic framework that allows us to investigate the notion of inference more carefully. Validity inference and truth inference are in some sense the extremal points in our framework. We investigate the relationship between various types of inference in our general framework, and consider the complexity of deciding if an inference rule is sound, in the context of a number of logics of interest: classical propositional logic, a nonstandard propositional logic, various propositional modal logics, and first-order logic.

STRATEGIES TO DEFEND A PROTAGONIST OF AN EVENT

2010 ◽  
Vol 19 (04) ◽  
pp. 439-464
Author(s):  
SARA BOUTOUHAMI ◽  
DANIEL KAYSER
Keyword(s):  
Natural Language ◽  
Experimental Validation ◽  
Answer Set Programming ◽  
First Order ◽  
Starting Point ◽  
First Results ◽  
Argumentative Strategies ◽  
Complete Set ◽  
Car Accident ◽  
Answer Set

We aim at controlling the biases that exist in every description, in order to give the best possible image of one of the protagonists of an event. Starting from a supposedly complete set of propositions accounting for an event, we develop various argumentative strategies (insinuation, justification, reference to customary norms) to imply the facts that cannot be simply omitted but have the "wrong" orientation w.r.t. the protagonist we defend. By analyzing these different strategies, a contribution of this work is to provide a number of relevant parameters to take into account in developing and evaluating systems aiming at understanding natural language (NL) argumentations. The source of inspiration for this work is a corpus of 160 texts where each text describes a (different) car accident. Its result, for a given accident, is a set of first-order literals representing the essential facts of a description intended to defend one of the protagonists. An implementation in Answer Set Programming is underway. A couple of examples showing how to extract, from the same starting point, a defense for the two opposite sides are provided. Experimental validation of this work is in progress, and its first results are reported.

scholarly journals A General Framework for Stable Roommates Problems using Answer Set Programming

2020 ◽  
Vol 20 (6) ◽  
pp. 911-925
Author(s):  
ESRA ERDEM ◽  
MÜGE FIDAN ◽  
DAVID MANLOVE ◽  
PATRICK PROSSER
Keyword(s):  
General Framework ◽  
Answer Set Programming ◽  
The Other ◽  
Stable Marriage ◽  
Stable Marriage Problem ◽  
Marriage Problem ◽  
Programming Paradigm ◽  
Formal Framework ◽  
The Stable Marriage Problem ◽  
Answer Set

AbstractThe Stable Roommates problem (SR) is characterized by the preferences of agents over other agents as roommates: each agent ranks all others in strict order of preference. A solution to SR is then a partition of the agents into pairs so that each pair shares a room, and there is no pair of agents that would block this matching (i.e., who prefers the other to their roommate in the matching). There are interesting variations of SR that are motivated by applications (e.g., the preference lists may be incomplete (SRI) and involve ties (SRTI)), and that try to find a more fair solution (e.g., Egalitarian SR). Unlike the Stable Marriage problem, every SR instance is not guaranteed to have a solution. For that reason, there are also variations of SR that try to find a good-enough solution (e.g., Almost SR). Most of these variations are NP-hard. We introduce a formal framework, called SRTI-ASP, utilizing the logic programming paradigm Answer Set Programming, that is provable and general enough to solve many of such variations of SR. Our empirical analysis shows that SRTI-ASP is also promising for applications.

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