The main aim of this paper is to create a semi-formal model of reasoning with cases in statutory interpretation. We introduce the notion of reasoning protocol as a frame for a set of elements used by relevant agents to justify their claims. Our model allows us to represent reasoning not only with factors, but also about the relevance of factors in deciding legal cases on the basis of statutory rules.
Hybrid reasoning with rules and cases has been the topic of interest for the AI
and Law community for more than two decades now, but it has been mostly
investigated in the context of Anglo-American law, which is hardly surprising
in the light of the signi cance of precedent in that particular legal environment
[
The model presented in our paper has a descriptive character which means that we do not introduce any mechanisms of argument creation or acceptance. Instead, we represent in a semi-formal manner the elements of reasoning that were explicitly used in the actual wording of judicial opinions. It should be noted that any loopholes and inconsequences of the parties' reasoning, may cause the same loopholes and inconsequences in their representation, which is the problem we intend not to focus on, taking into account the assumed descriptive perspective. 2
According to the Polish tax law, tax is levied on \net income" (dochod), which is
a surplus of total gross income (przychod) over the tax-deductible costs (article
7(2) of CITA [
Therefore, the taxpayer may often be interested to obtain an individual tax
ruling (ITR) resolving this problem (Art. 14b of the Tax Ordinance Act [
De nition 1 (Language) Let L be a de ned language being able to express terms and standard logical and set-theory connectives (_, ^, :, 2, etc. ) as well as function symbols.
facts.
De nition 3 (Case facts) A set Ck = fc1; :::cng C is referred to as case facts, that is, the subset of C that constitutes the considered fact situation.
By factors we understand propositions referring to elements of the case which provide reasons for a decision for either party. Factors are often referred to as \stereotypical fact patterns" to be distinguished from facts. Factors are binary (they may be present in a given case Ck or not) and if they are present, they always provide a reason for a decision for a given party. Superscripts we will indicate the name of a party whose interest is supported by the existence of a factor.
Similar to [
De nition 6 (Legal rule) Let ri be a legal rule i. Each rule is a pair ri = h ; i, where and are a w of L. is a condition of a rule and is a conclusion. By R we denote the set of all rules. By cond(r1) and conc(ri) we denote respectively condition and conclusion of a rule.
De nition 7 (Agents) Let IA 2 L be a set of propositions representing names
of various agents in legal discourse. By iai 2 IA we denote a given agent i.
De nition 8 (Interpretation) 2 L is a binary relation word denoting \is
interpreted as." An in-depth discussion of the functor can be found in [
De nition 10 (De ned relations) Let REL 2 L be a set of de ned relations between elements of L. For example: { Strict Incompatibility { Let and be statements of a language L. The two statements are strict incompatible SIN C( ; ) if they are incompatible and while one of them is not accepted, then the second one must be accepted. { Conditional su ciency { By SU F (fx; fy) we denote that factor fx is, defeasibly, a su cient condition for adoption of fy. { Irrelevance { Let fi be a factor and rk a legal rule. By irr(fi; rk) we denote that factor fi is explicitly considered as irrelevant to interpretation of rule rk. { Relevance { Let fi be a factor and rk a legal rule. By rel(fi; rk) we denote that factor fi is relevant to interpretation of rule rk.
De nition 11 (Hypotheticals) H( ) 2 L, where is a w of L, reads as \hypothetically, ". Intuitively, if an agent makes an expression H( ) this means that the agent poses a hypothesis that might or may have been the case. The expression H( ) 2 L means that H( ) is rejected. For any 2 L, H( ) i : .
It is important to note that it is not the aim of this paper to reconstruct a logical model of hypothetical or counterfactual thinking. The operator H is needed only to distinguish the contexts \ holds," expressed simply as , from the contexts like \ might have been the case" expressed as H( ).
De nition 12 (Argument) Let Aia be an argument created by agent ia 2 IA.
i Each argument is a tuple Aia = hname; ; i, where name 2 L is an argument i name, is a set of w of L, and is w of L. is a set premises of an argument, is a conclusion. By ARG we denote the set of all arguments. Intuitively by Aiia = hname; ; i, we denote that supports . By prem(name) 2 L we denote the set of premises of argument named name, by concl(name) 2 L, and author(name) 2 L we will denote functions returning conclusion and author of argument Aiia: if Aiia = hname; ; i, then prem(name) = , concl(name) = , and author(name) = ia.
De nition 13 (Reasoning protocol) Let P ROTia = hname; Cl; Rs; Cf; Rf; Rel; Cs; Sf; Is; Carg; Conci be a 11-tuple representing of reasoning protocol of agent ia, where: 0. name 2 L { is a name of the protocol; 1. Cl 2 L { is a claim which agent ia is going to prove; 2. Rs R { is a set of legal rules which agent ia needs to prove the claim; 3. Cf C { is a set of case facts (actual state of a airs); 4. RRel F { is a set of relevance relations of two kinds: rel(fi; rk) and irr(fi; rk); 5. ORel L { is a set of other de ned relations between factors (for example incompatibility or strict incompatibility relations) which are relevant to the case. We assume that in ORel can be used factors which are in the relations from set RRel; 6. Cs L { is a set of adopted classi cation statements; 7. Sf F { is a set of satis ed factors i.e. factors which can be accepted (on the basis of Cf ); 8. Is { is a set of adopted interpretive statements; 9. Carg ARG { is a set of subsumption arguments, i.e. arguments necessary to support the conditional part of a legal rule; 10. Conc 2 L { is a nal conclusion, in most cases Conc = Cl. Additionally we assume a set of functions returning particular sets of elements of a protocol. For example, function Cl(name) 2 L returns claim of protocol named name.
De nition 14 (Case) Let CASEi L be a case i represented by a set of names of reasoning protocols used in the case. We assume that protocols in the case are ordered. Let OCASEi L be a partial order of elements of CASEi. The order of protocols represents the power of the authors of particular reasoning protocols over other authors. For example, a claim of tax authority (and its arguments) is stronger than a claim of taxpayer; decision of a Court is stronger than a claim of tax authority, etc. By CASE we denote the set of all cases. The representation of a case is a key point of our model. The output of a previous case includes not only the factors, rules and nal decision, but also the more extensive information represented in Reasoning Protocols. In a new case, the Court, can construct an argument not only on the basis of the nal decision, but also on the basis of the mechanisms used in arguments justifying a previous decisions. 4
We use the model outlined in the previous section to represent the reasoning of relevant agents in two cases, namely, the judgment of 7 judges panel of the SAC of 17 June 2013 (II FSK 702/11, hereafter: Judgment 1) and the judgment of the VAC of Rzeszow of 23 October 2018 (I SA/Rz 741/18, hereafter: Judgment 2). Judgment 1 is particularly interesting because the SAC expressed an opinion on the appropriate interpretation of the statutory rule concerning the costs of representation. The modelling of Judgment 2 shows how the preceding decision practically constrains the legal reasoning of relevant agents even though no stare decisis principle is applicable in this context.
Judgment 1 The legal context for the case is provided by the statutory rule r1, based on art. 16.1.28 of the CITA as discussed above in Section 2: cond(r1) = representation costs including costs related to purchase of catering services or f ood or beverages including alcoholic ones conc(r1) = not tax deductible costs In the case that gave grounds for Judgment 1, the agent taxpayer (TP) was interested to obtain an ITR to the e ect that the costs incurred by TP are not representation costs (the positive conditions of tax-deductible costs were assumed to be met). In the motion for ITR, TP outlined a hypothetical case C1 comprising the facts that TP, being a company, organizes business meetings with its (potential) contractors and incurs the purchase of catering services. The signi cant catering expenses are incurred when meetings take place in restaurants, so the signi cant facts may be presented as follows: C1 = fc1; c2g where c1 = business meetings in restaurants, c2 = taxpayer incurs catering expenses During the time the motion of ITR was led, the case law, concerning what factors should be considered in the process of quali cation of a given cost as an instance of representation cost, was unstable. This state of a airs gave rise to proceedings before the Tax Authority, The Voivodeship Administrative Court and the Supreme Administrative Court, which eventually referred the case to be decided by the grand jury (7 judges panel).
The SAC was considering whether the legal rule r1 (category Rs) should be applicable to the presented case facts (Cf ). Unlike in the previous case law (which we do not discuss here because of space limitations), the SAC stated the factor relevant for deciding whether a given cost is a representation cost: the exclusive or main goal of this cost must be the building of image by the taxpayer. If this factor is not met, the tax authorities should assume that the cost was met for business purposes (provided that the positive conditions of tax deductibility were met, which was assumed in the present case). In a given case SAC recognizes two relevant factors: f1 = image building exclusive or main purposeT A and f2 = business purposeT P , while category (ORel) de nes the strict incompatibility relation between them. In the context of the case facts the court held that the factor f1 should not be considered to apply only because the meetings took place in restaurants or because they involved the purchase of catering. The adoption of f1 as the only factor relevant for the interpretation of the rule condition imposes a degree of argumentative burden on tax authorities: it is di cult to su ciently argue that the cost of image building as its exclusive or main goal. The interpretive standards adopted by the SAC, in particular in judgments enacted by the grand jury, are practically di cult to challenge, taking into account that if properly complained, the future case will eventually be heard by the SAC. The Reasoning Protocol of the SAC (SAC judg1 2 CASESAC judg1) may be presented as follows.
Category Content name SAC judg1
Cl :conc(r1) Rs r1
Cf C1 = fc1; c2g RRel rel(f1; r1), rel(f2; r1) ORel SIN C(f1; f2)
Cs S1 = :sat(C1; f1), S2 = sat(C1; f2) Sf f2
Is IS1 = f1 cond(r1) Carg As1ac =< a1; fIS1; :f1; f2g; :cond(r1) >
Conc :conc(r1) Judgment 2 In the fact situation that gave rise to the issuance of Judgment 2, the TP applied for an ITR concerning the following circumstances: the TP acting as a company (employer) organizes integration events both for its workers employed on the basis of employment contract and for its B2B contractors. The organization of the integration events requires purchase of catering services for the participants. The TP argues that such costs do not amount to representation costs. However, the TA disagreed with the TP with regard to the costs related to participation of B2B contractors on the basis that they are actually third parties. The set of relevant case facts includes one element: C2 = fc3g, c3 = intergration events f or B2B contractors Category Content name T P judg2
Cl :conc(r1) Rs r1
Cf C2 RRel rel(f1; r1), rel(f2; r1) ORel SIN C(f1; f2)
Cs S3 = :sat(C2; f1), Sf f2
Is IS1 = f1 cond(r1) Carg At2p =< a2; fIS1; :f1; f2g; :cond(r1) >
Conc :conc(r1) As we can easily ascertain, the TP followed strictly the Reasoning Protocol employed by the SAC in Judgment 1. Obviously, the case facts that gave rise for the motion for the ITR were di erent, but the TP adopted relevant factors (RRel) and the de ned relation (ORel) in accordance with the Reasoning Protocol SAC II FSK 702/11. The TA basically followed the Reasoning Protocol designed by the SAC in the II FSK 702/11 case (Judgment 1) because it adopted the same interpretive statement and it also did not reject any of the factors accepted by the SAC. However, the TA also added an additional factor and additional relation between factors. The TA conceded that the B2B contractors are third parties with regard to TP, and that the existence of such a factor implies the existence of the factor f4, that is, if the newly designed factor is satis ed, the f4 factor is also satis ed. The factor designed by the TA may be represented as follows: f1:1 = costs incurred f or the third partyT A Since the factor f1:1 is attached to f1 as an immediate lower-level factor, there is a relation SU F (f1:1; f1) between them. The Reasoning Protocol of the TA:
Category Content name T A judg2
Cl conc(r1) Rs r1
Cf C2 RRel rel(f1; r1), rel(f2; r1), rel(f1:1; r1) ORel SIN C(f1; f2), SU F (f1:1; f1)
Cf S4 = sat(C2; f1:1), S5 = sat(f1:1; f1), Fs f1:1, f1
Is IS1 = f1 cond(r1) Carg At3a =< a3; fIS3; f1:1; f1g; cond(r1) >
Conc conc(r1) As we can see, the TA did not delete any information from the categories RRel, ORel, or Is from Reasoning Protocol as designed by the SAC in Judgment 1, but instead attempted to develop it by establishing a new factor f1:1 understood as a su cient condition for adoption of f1.
The TP led a complaint to the VAC. The VAC agreed with the TP and applied legal meta-reasoning by pointing out that the TA had introduced an inappropriate standard. The Reasoning Protocol developed by the VAC was identical to the one employed by the TP, so instead of repeating it here, let us reconstruct the meta-argument based on the discrepancy of the Reasoning Protocol the TA was supposed to use and the Reasoning Protocol it actually used. Category Content name V AC judg2
Cl :conc(r1) Rs r1
Cf C2 RRel rel(f1; r1), rel(f2; r1), irr(f1:1; r1) ORel SIN C(f1; f2)
Cf S6 = :sat(C2; f1); S7 = sat(C1; f1:1), Fs f2
Is IS1 = f1 cond(r1) Carg A4vac =< a4; fH(rel(f1:1; f1) 2 RRel(SAC judg1))g;
S7 2 Cs(SAC judg1) > A5vac =< a5; f:(S7 2 Cs(SAC judg1); inc(:(S7 2 Cs(SAC judg1)); H(rel(f1:1; f1) 2 RRel(SAC judg1))g;
H(rel(f1:1; f1) 2 RRel(SAC judg1)) A6vac =< a6; f H(rel(f1:1; f1) 2 RRel(SAC judg1)))g; :A(7vraecl=(f<1:1a; 7r;1f):2reRl(Rfe1:l1(;SrA1)C2jRudRge1l)()S>AC judg1)g; irr(f1:1; r1) > A8vac =< a8; firr(f1:1; r1); f1:1 2 prem(a3); r1 2 Rs(T A judg2); a3 2 Carg(T A judg2)g; :a3 >
A9vac =< a9; fIS1; :f1; f2g; :cond(r1) >
Conc :conc(r1) The VAC basically agreed with the TP and disregarded the reasoning of the TA, which led to avoiding of the ITR provided by the latter agent. One can notice that TA did not go straightforwardly against the Reasoning Protocol designed by the SAC, but added new elements to its arguments (factor f1:1, the relation SU F (f1:1; f1)), e ectively narrowing the scope of tax-deductible costs. On the rst sight, such an extension of the set of relevant elements was not precluded by the SAC. The VAC provided an additional argument for its position by using the SAC's opinion to justify that the Reasoning Protocol developed by the TA was fallacious. The argument of the VAC is based on hypothetical reasoning. First, the VAC indicates that if the SAC considered f1:1 to a be a relevant factor for interpretation of the rule r1, it would also have held that the factor f1:1 was satis ed by the case C1, because obviously, the meetings in restaurants in C1 were organized for third parties (a4). Because, such a classi cation statement was not recognized by the SAC, the hypothetical statement that the f1:1 would be the relevant factor should be falsi ed (a5). On this basis, the VAC drew an explicit conclusion that the factor f1:1 is not relevant for the interpretation of the rule (a6) and therefore it is irrelevant in this context (a7). The argument a7 attacks one of the premises of the TA's argument a3, which invalidates the latter agent's reasoning.
The set CASEjudg2 = fT P judg2; T A judg2; V ACjudg2g contains all reasoning protocols of all parties which take part in the discourse. Both T P judg2 and V ACjudg2 have the same conclusion (:cond(r1)), which is in con ict with the conclusion of T A judg2 (cond(r1)). We also assume that the Court has power over both parties which can be represented by order OCASEjudg2 = (V ACjudg2 > T P judg2); (V ACjudg2 > T A judg2), thanks to which the Court's conclusion prevails over the conclusion of the Tax Authority. 5
This paper has two main contributions. The rst one is the development of the notion of Reasoning Protocol and the second one is the investigation of selected patterns of case-based judicial reasoning in the context of statutory interpretation as it is understood in continental legal culture. We investigated cases where not only factors played a role in forming interpretive sentences, but also where reasoning about the relevance of factor played a pivotal role in judicial reasoning. The Reasoning Protocol is a tool for descriptive systematization of legal reasoning. It does not aim, per se, to be a computational model of legal argument, but rather a means to systematize the elements of reasoning explicitly used in the text of judicial opinions. Therefore, it is designed rst and foremost to study past decisions and to systematize knowledge about the reasoning patterns used in legal practice, not only by courts, but also by other agents whose reasoning is reported in judicial opinions. The Reasoning Protocol is designed to represent incomplete, enthymematic reasoning. However, it may serve as a starting point for reconstruction of premises that are further used to feed computational models of legal reasoning.The second contribution of the paper is the investigation into the structure of reasoning with cases in the continental legal culture environment.
Whilst the problem of justifying legal interpretation with di erent classes of
arguments (linguistic, systemic, and functional) has already earned considerable
attention from the AI and Law community, the role of factor-based reasoning
in this context, analyzed from the descriptive point of view, has remained
neglected. In this contribution we have purposefully focused on the problem how
the determination of factors in a landmark case (Judgment 1) in uenced the
reasoning in a following case (Judgment 2). We have investigated how the Tax
Authority attempted to narrow the scope of interpretation of the notion of
taxdeductible costs by introducing new elements to the Reasoning Protocol content
xed by the SAC, and how the VAC criticized this attempt by constructing and
applying a complex hypothetical argument. The analysis reveals important
parallelism between common-law case-based reasoning on the one hand and civil
law case -based reasoning on the other hand. In both contexts (1)
hypothetical reasoning is important in the context of case-based reasoning and (2) the
relevant agents may attempt to draw consequences from the features that
distinguish the present case from the previous one. The use of the hypothetical
reasoning has revealed an important and methodologically challenging issue: the
TA attempted to build its argument on assumed information that might have
been implicit in the leading case decided by the SAC. The new case was based on
a di erent set of case facts, which might have lead to satisfaction of di erent set
of factors. However, the crucial issue was whether the factor \discovered" by the
TA (f1:1) was legally relevant in this context at all. Testing these assumptions
led the VAC to the conclusion that the reasoning of the TA was fallacious. The
TA added unfounded information to the Reasoning Protocol and thus followed a
wrong Reasoning Protocol which lead to avoidance of its decision (ITR). In order
to focus on the phenomenon described above, we have purposefully ommitted
the issues of interpretive argumentation [
This paper shows how reasoning with and about factors in the context of
statutory interpretation may be described with a tool referred to as Reasoning
Protocol. This tool enables researchers to systematize and compare the reasoning
used by di erent agents that arguing in legal cases. With this tool, we have
analyzed how factors are used in statutory interpretation and how the issue of
factor relevance is addressed in this context. In the discussed example, the
factors provided the basis for formulation of interpretive statements. We have also
shown how the relevance of certain factors is argued in the context of statutory
interpretation and how hypothetical argumentation is used to justify the
conclusions in this area. As for the directions of further research, three of them should
be mentioned. First, we intend to broaden the scope of analyzed cases and the
information represented in the Reasoning Protocol. The scope of information
represented in the Reasoning Protocol will be extended to encompass, inter alia,
the interpretive arguments and value-based reasoning. The adopted
methodology will be also applied in other domains of law, to evaluate the generalizability
of the present approach. It is also not excluded that the analysis of a broader
set of cases will enable the use of more complex types of case-based reasoning
knowledge representation, such as factors with magnitudes or dimensions.
Second, the information and reasoning patterns found in Reasoning Protocols may
be integrated with a methodologically di erent approach, that is, computational
modelling of legal argument, enabling automation of reasoning, in such systems
as ASPIC+ [
The work of Michal Araszkiewicz and Tomasz Z_urek was part of the project \Legislative errors and the comprehensibility of legal texts" nancially supported by the National Science Centre; agreement no. UMO-2018/29/B/HS5/01433