Temporal Preference Models and their Deduction-based Analysis

for Pervasive Applications

Radosław Klimek

AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland

Keywords:

Preference Modeling, Context-aware Applications, Patterns, Temporal Logic, Deduction, Semantic Tableaux.

Abstract:

This work concerns preference models and their formal analysis using a deductive approach, i.e. temporal

logic for both speciﬁcation and veriﬁcation, and the semantic tableaux method for reasoning. The architecture

of an automatic and deduction-based veriﬁcation system for preference models is also proposed. It allows

analysis of both desired properties of models and their semantic contradictions. Preference models are built

from predeﬁned patterns which enable automatic generation of logical speciﬁcations for preferences.

1 INTRODUCTION

Preference modeling enables customization of soft-

ware behavior to a user’s needs. Preference models

are particularly important in pervasive computing and

ubiquitous computing which are paradigms related

to the behavior of software highly oriented towards

users and their needs, assuming also the omnipres-

ence of computing. Preference modeling is essential

and crucial, and constitutes a type of bridge between

a support-oriented user and a system which is itself

able to provide support.

The model of preference might be constructed us-

ing fuzzy sets, classical logic and multi-valued logic.

Classical logic, and particulary rule-based systems,

are especially popular while non-classical logic and

especially temporal logic, are rather less popular.

However, temporal logic is a well established formal-

ism for describing reactivity. At the same time, a

typical pervasive application should be characterized

by reactivity and ﬂexibility in adapting to preference

changes on the user’s side. After building a prefer-

ence model in temporal logic, one can analyze it using

a deductive approach. The goal is to search, if possi-

ble, for contradictions in a model or to infer some-

thing about the correctness of the preference objec-

tives. Temporal logic enables illustration the dynamic

aspect of preferences over ﬂows of time.

Motivations and Contributions

The general motivation is the lack of satisfactory and

documented results of using temporal logic and the

deduction-based approach for formal analysis of pref-

erence models. Another motivation factor is the lack

of tools for automatic extraction of logical speciﬁca-

tions for preference models.

The main contributions are the automation of the

generation process of logical speciﬁcations for pref-

erence models, predeﬁned preference patterns, and

generation algorithm for preference patterns. Another

contribution is the use of a non-standard method for

deduction for preferences.

Related Works

Instead of discussion of related works, beyond the

fundamental work by

Ozt¨urk et al. (

Ozt¨urk et al.,

2005), let us pay attention on work by Fong et

al. (Fong et al., 2011). It includes an excellent section

on the state of the art of preference modeling. It is a

highly in-deep and comprehensive review. This work

is an attempt to extend the view of problems of pref-

erence modeling expressed in (Fong et al., 2011) by

introducing temporal logic and the semantic tableaux

method.

2 MODEL OF PREFERENCES

Preference models are discussed below. The proposed

preference model is based on predeﬁned patterns of

rules which are shown in Fig. 1. These rules are ex-

pressed in temporal logic. Temporal logic and the de-

ductive system are discussed in section 3. However, it

is assumed that well-formed and syntactically correct

131

Klimek R..

Temporal Preference Models and their Deduction-based Analysis for Pervasive Applications.

DOI: 10.5220/0004314901310134

In Proceedings of the 3rd International Conference on Pervasive Embedded Computing and Communication Systems (PECCS-2013), pages 131-134

ISBN: 978-989-8565-43-3

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

(a) Sequence

f2 f3

−

(b) Branch

−

Figure 1: Patterns for preferences.

temporal logic formulas have already been deﬁned,

c.f. (Wolter and Wooldridge, 2011).

Preference models consist of some basic patterns.

A pattern is a predeﬁned solution for a special con-

text where there are preference issues. They are gen-

erally indicated as pat(), where pat is a name of a

given pattern, and their parameters are included in

parentheses. The following three patterns are con-

sidered: Branch, SimpleBranch and Sequence. It is

a kind of illustration of the if-then scheme. Pat-

terns of behaviors and preferences can be nested. It

follows from the scenario of multi-stage decision-

making. A basic set of patterns Σ is a set of temporal

logic formulas describing both liveliness and safety

properties of a pattern. A set of three patterns, i.e.

Σ = {Branch, SimpleBranch, Sequence}, will be con-

sidered. Let us deﬁne temporal properties for these

patterns. Hence, set Branch( f

, f

) = { c( f

) ⇒

♦ f

∧ ¬♦ f

, ¬c( f

) ⇒ ¬♦ f

∧ ♦ f

, ¬( f

∧ ( f

∨

))} describes property of the Branch pattern

and SimpleBranch( f

, f

) = {c( f

) ⇒ ♦ f

, ¬c( f

) ⇒

¬♦ f

, ¬( f

∧ f

)} the SimpleBranch pattern. Set

Sequence( f

, f

) = { f

⇒ ♦ f

, ¬( f

∧ f

)} deﬁnes

the Sequence pattern. For the meanings of these pat-

terns, refer to Fig. 1. Formulas f

, f

etc. are atomic

formulas for a pattern, and constitute some formal ar-

guments for these pattern. ♦ f means that sometime

(or eventually in the future) activity f is completed.

In addition, c( f) means that the logical condition as-

sociated with activity f has been evaluated and is sat-

isﬁed.

The entire preference model can be written in the

form of logical expressions, which is similar to some

well-known regular expression. The goal is to write

preference models in a concise and literal notation. A

logical expression W

is a structure created using the

following rules:

• every elementary set pat(a

), where i > 0 and ev-

ery a

is an atomic formula, is a logical expres-

sion,

• every pat(A

), where i > 0 and every A

is either

– an atomic formula a

, where j > 0, or

– a set pat(a

), where j > 0 and a

is an atomic

formula, or

– a logical expression pat(A

), where j > 0

is also a logical expression.

Any logical expression may represent an arbitrary

structure of patterns and examples of this are expres-

sion Branch(a, SimpleBranch( f, g), c) and expres-

sion Sequence(Branch(a, b, c), SimpleBranch(d, e)).

In the ﬁrst case, the combination (and nesting) of

two branchings is considered, i.e. the ordinary and

the simple one. In this expression, a and f are the

conditions. In the second case, the sequence of two

branchings is considered.

An individual preference may belong to a set of

preferences P, i.e. P = {p

, p

, ... p

}, where p

is a

preference which is expressed as a single logical ex-

pression, i.e. p

= W

3 DEDUCTION SYSTEM

The logical background is discussed further below.

The important argument for a deductive approach is

how natural it is for human beings and it is used

commonly and intuitively in everyday life. Tempo-

ral Logic TL is a valuable formalism, e.g. (Wolter

and Wooldridge, 2011), which has strong applica-

tions for the speciﬁcation and veriﬁcation of mod-

els. It exists in many variations, however, consid-

erations in this paper are limited to the Linear Tem-

poral Logic LTL, i.e. logic for which the time struc-

ture is considered as linear. Furthermore, considera-

tions are limited to the smallest, or minimal, temporal

logic, e.g. (Chellas, 1980), also known as temporal

logic of class K. The following formulas may be con-

sidered as signiﬁcant examples of minimal temporal

logic: quest ⇒ ♦answer, (action ⇒ ♦react), ♦liv,

¬(bad) or ¬(ev1∧ (ev2∨ ev3)), etc.

Semantic tableaux is a decision-making procedure

for checking satisﬁability of a formula. The method

is well known in classical logic but it can also be ap-

plied in modal and temporal logics (d’Agostino et al.,

1999). The method is based on formula decomposi-

tions. At the end of the decomposition procedure, all

branches of the received tree are searched for contra-

dictions. When all branches of the tree have contra-

dictions, it means that the inference tree is closed. If

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[1,−]

1 : (f ⇒ ♦c) ∧ (c ⇒ ♦p) ∧ ¬(p∨ ¬q) ∧ ¬(¬ f ∧ q)

[2,1]

1 : ( f ⇒ ♦c)

[3,1]

1 : (c ⇒ ♦p)

[4,1]

1 : ¬(p ∨ ¬q)

[5,1]

1 : ¬(¬f ∧ q)

[6,2]

1 : ¬f

[9,3]

1 : ¬c

[15,4]

1.(x) : ¬(p∨ ¬q)

[18,15]

1 : ¬p

[19,15]

1 : q

[24,5]

1.(y) : ¬(¬ f ∧ q)

[25,24]

1 : f

[26,24]

1 : ¬q

[10,3]

1 : ♦p

[11,10]

1.[p] : p

[16,4]

1.(x) : ¬(p∨ ¬q)

[20,16]

1 : ¬p

[21,16]

1 : q

[7,2]

1 : ♦c

[8,7]

1.[c] : c

[12,3]

1 : ¬c

[13,3]

1 : ♦p

[14,13]

1.[p] : p

[17,4]

1.(x) : ¬(p∨ ¬q)

[22,17]

1 : ¬p

[23,17]

1 : q

Figure 2: Truth tree of the inference process.

the negation of the initial formula is placed in the root,

this leads to the statement that the initial formula is

true. This method has some advantages over the tra-

ditional axiomatic approach. In the classical reason-

ing approach, starting from axioms, longer and more

complicated formulas are generated and derived. For-

mulas become longer and longer step by step, and

only one of them will lead to the veriﬁed formula.

The method of semantic tableaux is characterized by

the reverse strategy. The method provides, through

so-called open branches of the semantic tree, infor-

mation about the source of an error, if one is found,

which is another and very important advantage of the

method.

Let us consider the following example. The pref-

erence model is constructed from a natural text: If

he buys a Ferrari then he sometime smokes a Cuban

cigar. If he smokes a Cuban cigar then he some-

time drinks a Dom Perignon champagne. However,

it is never so that he drinks a Dom Perignon cham-

pagne or he does not quit drinking alcohol. More-

over, it is not so that he does not buy a Ferrari and

quit drinking alcohol. The following simple sen-

tences are extracted: “to buy a Ferrari” – f, ‘ ‘to

smoke a Cuban cigar” – c, “to drink a Dom Perignon

champagne” – p, and “to quit drinking alcohol” – q.

Then, the following formulas of temporal logic are

extracted: ( f ⇒ ♦c) and (c ⇒ ♦p) and ¬(p ∨ ¬q)

and ¬(¬ f ∧ q). These formulas express the prefer-

ence model. The ﬁrst two formulas express the live-

ness aspect of the model, and the last two formulas

express the safety aspect of the model. The prefer-

ence model is analyzed using the method of sematic

tableaux, c.f. Fig. 2. All branches contain contradic-

tions (×). This means there is no valuation for ex-

tracted propositions that satisﬁes the formula which

is placed in the tree root. The preference model is

semantically contradictory.

4 TOWARDS AUTOMATION

Building a logical model for preferences in the form

of temporal logic formulas, i.e. P = {p

, p

, ... p

enables examination two important aspects of the sys-

tem:

1. semantic contradiction, or

2. correctness of the model due to some properties.

Analysis of semantic contradiction is shown in the

previous section. In turn, formal veriﬁcation of prop-

erties of the preference model leads to the analysis of

formula p

∧. . . ∧ p

⇒ Q, where Q is a desired prop-

erty of the preference model {p

, p

, ... p

The system of automatic inference on preference

models is proposed in Fig. 3. The Modeler module

allows (instead of natural language) the preparation

a preference model using preference patterns shown

in Fig. 1. The output of the Modeler is preference

models expressed as logical expressions W

The next module is the Generator module and its

inputs are logical expressions W

and predeﬁned set

of preference patterns Σ. The output is a logical spec-

iﬁcation L understood as being a set of temporal logic

TemporalPreferenceModelsandtheirDeduction-basedAnalysisforPervasiveApplications

133

MODELER

GENERATOR

PROVER

Y/N

Contr.

Figure 3: Deduction system.

formulas. The sketch of the generating algorithm is

the following:

1. at the beginning, the logical speciﬁcation is

empty, i.e. L =

2. the most nested pattern or patterns are processed

ﬁrst, then the least nested patterns are processed

one by one, i.e. patterns that are located more to-

wards the outside;

3. if the currently analyzed pattern consists only of

atomic formulas, the logical speciﬁcation is ex-

tended, by summing sets and by formulas linked

to the type of the analyzed pattern pat(), i.e. L =

L∪ pat();

4. if any argument is a pattern itself, then the logical

disjunction of all its arguments, including nested

arguments, is substituted in place of the pattern.

The above algorithm refers to similar ideas in

work (Klimek, 2012). Let us supplement the algo-

rithm with some examples. The example for the

step 3: Seq(p, q), givesL = {p ⇒ ♦q, ¬(p∧q)} and

Branch(a, b, c) gives L = {c(a) ⇒ ♦b∧¬♦c, ¬c(a) ⇒

¬♦b ∧ ♦c, ¬(a ∧ (b ∨ c))}. The example for the

step 4: Sequence(Branch(a, b, c), d) leads to L =

{c(a) ⇒ ♦b ∧ ¬♦c, ¬c(a) ⇒ ¬♦b ∧ ♦c, ¬(a ∧ (b ∨

c)), (a ∨ b∨ c) ⇒ ♦d, ¬((a∨ b ∨ c) ∧ d)}.

The last module is the Prover module that works

using the semantic tableaux method. The inputs for

the Prover are a logical speciﬁcation L and a query Q

which is a simple temporal logic formula which ex-

presses the desired property of the preference model.

(This formula can be prepared using a simple text ed-

itor.) The Prover provides examination for two cases:

1. correctness of the model due to some properties,

i.e. the formal veriﬁcation of the formula:

∧ . . . ∧ p

⇒ Q (1)

2. semantic contradiction, i.e. the formal analysis of

the formula:

∧ . . . ∧ p

(2)

In the case of correctness, the negation of the for-

mula 1 is placed in the root and the Yes/No output is

produced. In the case of contradiction, the formula 2

is placed in the root and the information about the se-

mantic contradiction is produced.

5 CONCLUSIONS

The work presents a new approach to the formal anal-

ysis of preference models using temporal logic and

the semantic tableaux method. Future work may in-

clude the implementation of the logical speciﬁcation

generation module and a deduction engine. The ap-

proach should results in a CASE software providing

modeling preferences.

ACKNOWLEDGEMENTS

This work was supported by the AGH UST internal

grant no. 11.11.120.859.

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