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Logical Vs. Natural Language Conjunctions in Czech: a Comparative Study

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Logical Vs. Natural Language Conjunctions in Czech: a Comparative Study ITAT 2016 Proceedings, CEUR Workshop Proceedings Vol. 1649, pp. 68–73 http://ceur-ws.org/Vol-1649, Series ISSN 1613-0073, c 2016 K. Prikrylová,ˇ V. Kubon,ˇ K. Veselovská Logical vs. Natural Language Conjunctions in Czech: A Comparative Study Katrin Prikrylová,ˇ Vladislav Kubon,ˇ and Katerinaˇ Veselovská Charles University in Prague, Faculty of Mathematics and Physics Czech Republic {prikrylova,vk,veselovska}@ufal.mff.cuni.cz Abstract: This paper studies the relationship between con- ceptions and irregularities which do not abide the rules as junctions in a natural language (Czech) and their logical strictly as it is the case in logic. counterparts. It shows that the process of transformation Primarily due to this difference, the transformation of of a natural language expression into its logical representa- natural language sentences into their logical representation tion is not straightforward. The paper concentrates on the constitutes a complex issue. As we are going to show in most frequently used logical conjunctions, and , and it the subsequent sections, there are no simple rules which analyzes the natural language phenomena which∧ influence∨ would allow automation of the process – the majority of their transformation into logical conjunction and disjunc- problematic cases requires an individual approach. tion. The phenomena discussed in the paper are temporal In the following text we are going to restrict our ob- sequence, expressions describing mutual relationship and servations to the two most frequently used conjunctions, the consequences of using plural. namely a (and) and nebo (or). 1 Introduction and motivation 2 Sentences containing the conjunction a (and) The endeavor to express natural language sentences in the form of logical expressions is probably as old as logic it- The initial assumption about complex sentences contain- self. A very important role in this process is being played ing the conjunction a (and) is inspired by the properties by natural language conjunctions and their transformation of the corresponding logical connective and – we suppose into logical connectives. The conjunctions are much more that the two clauses connected by the conjunction express ambiguous than logical connectives and thus it is neces- two situations which are valid at the same time. This really sary to analyze their role in natural language sentences, in holds in a number of complex sentences, as for example various contexts and types of texts. This paper presents here: a step towards such analysis for one particular language - Lev je koˇckovitá šelma a žije v Africe. (1) Czech. (Lion is a feline and it lives in Africa.) Let us recall that the fundamental task of logic is to set rules and methods for inferencing and referencing. On the Jana je ve škole a Honza leží nemocný v posteli. other hand, natural languages serve primarily for commu- (2) nication. Speakers can reach and agreement or understand (Jana is in a school and Honza lies ill in bed.) each other even without a strict adherence to preset rules In the sentence 1 we have used the so called gnomic (regardless whether they are morphological, grammatical present1. The truth value of the whole sentence is TRUE or stylistical). A human brain can obtain substantial in- only in case that both clauses are TRUE, regardless of the formation also from ill-formed sentences what actually context or current situation. makes them to fulfill their main goal, to serve as a tool Complex sentences with gnomic present constitute for communication. On the other hand, Noam Chomsky probably the simplest case. It is not necessary to investi- introduced in [1] also a famous example Colourless green gate whether the clauses are true or what are the conditions ideas sleep furiously – a grammatically well-formed sen- under which they might become true – they are simply true tence which does not have any meaning and thus it cannot either always or never. Such sentences can be transformed serve the communication task. into a logical representation in a simple and straightfor- Sentences in any natural languge are not isolated, their ward manner.2 In the logical representation of the exam- meaning typically depends on the context in which they ple above we would of course use the construction A B appear, on the way how they are pronounced or even on for the conjunction a (and). ∧ some external factors as, e.g., gestures which accompany it. Natural languages also evolve in time according to the 1Present tense can be used also for the so called extratensal pro- needs of the language community and although each nat- cesses which are valid always, regardless of the current situation. In our example we describe properties of an animal species and its habitat. ural language has a set of generally applicable rules (syn- 2Let us point out that mathematical theorems typically contain tactic, stylistic, morphological etc.), there are many ex- gnomic present. Logical vs. Natural Language Conjunctions in Czech: A Comparative Study 69 The sentence 2 describes two situations being TRUE ex- Or, we could drop the initial part which we may con- actly in this moment3. The truth value of both sentences sider to be implicitly present: can be determined by a reference from the language to a real–world, where we will find out whether both clauses Jana je ve škole, a souˇcasnˇeHonza leží describe a valid situation.4 nemocný v posteli. (6) None of the two clauses from the sentence 2 is abso- (Jana is in the school, and, at the same lutely true (Jana does not spend every minute of her life in time, Honza is lying ill in bed.) the school and Honza is not ill forever). However, when we utter any of these two statements, we do not mean that Into such template it is possible to insert also the com- Jana should stay all the time in the school. The use of the plex sentence introduced above: present tense implicitly carries the information that she is there just now, in this moment. If we accept that in order Jana byla vˇcera ve škole a souˇcasnˇeHonza to determine the truth value, we have to look into the real vˇcera ležel nemocný v posteli. (7) world and also take into the account the time when the sen- (Jana was in a school yesterday and, at the same tence was uttered, we could paraphrase the sentence into a time, Honza was lying ill in bed yesterday.) more unambiguous variant for example like this: All the complex sentences mentioned above can Jana je právˇeted’ ve škole a Honza nyní leží schematically be described in the form A B. The fact nemocný v posteli. that we can express the mutual relationship∧ of clauses by (3) (Jana is just now in the school and Honza is means of a logical scheme actually means that we can now lying ill in bed.) work with them according to logical rules. For example, logical conjunction is commutative – and we really can – i.e. with the added information about time. Such sen- swap the order of clauses in our complex sentence and still tence would then correspond to the logical scheme of the retain the original truth value. conjunction : A B.5 Natural languages∧ use, of course, also other tenses – 2.1 Violation of a temporal sequence what if we would like to express the same content in the past, for example yesterday? Unfortunately, the conjunction a (and) doesn’t appear only in sentences describing actions which are happening in the Jana byla vˇcera ve škole a Honza vˇcera ležel same moment. All of the following sentences contain a nemocný v posteli. (4) (and) as its main conjunction: (Jana was in a school yesterday and Honza Honza spadl a zlomil si ruku. was lying ill in bed yesterday.) (8) (Honza fell and broke his arm.) On the first sight, there seems to be no substantial problem. The only difference seems to be in the fact that we are not Jana odemkla a vešla do bytu. (9) referring to a current moment, but to the moment in the (Jana unlocked and entered the flat.) past (in this case, yesterday). However, what if Honza will recover till the next day, will such sentence have the same Šli jsme na výstavu a potom do kina. truth value also tomorrow? (We have visited an exhibition and (10) Regardless to what time the expressions refer to, we are then we went to a cinema.) interested in them only if they are TRUE in this current moment. We should thus simplify our sentence rather in These sentences apparently aren’t commutative. The or- the following way: der of clauses cannot be swapped without affecting the truth value or meaning of the whole sentence. The rea- Právˇeted’ platí, že Jana je ve škole, a souˇcasnˇe, son is obvious – both clauses are ordered into a temporal že Honza leží nemocný v posteli. sequence. (5) (Just now it is true that Jana is in the school, The conjunction a (and) isn’t a logical conjunction in these sentences, although it fulfills one fundamental basic and, at the same time, Honza is lying ill in bed.) condition – if the whole sentence is supposed to be true, 3Of course, only if it is true that Jana is just now in the school and then both clauses also have to be true. Honza lies ill in his bed. The propositional logic nevertheless cannot cope with 4Determining the truth value of natural language expressions is stud- sentences of this kind. We might be tempted to attempt to ied by epistemology, a simple explanation can be found for example in solve this issue by means of the conditional construction [2]. 5If we would like to consider tiniest details, we would have to con- Když..., (pak) ..
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